On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach
Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describ...
Saved in:
| Published in | Journal of mathematical biology Vol. 83; no. 6-7; p. 64 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results. |
|---|---|
| AbstractList | Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results. Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results. |
| ArticleNumber | 64 |
| Author | Pasquini, Mirko Angeli, David |
| Author_xml | – sequence: 1 givenname: Mirko orcidid: 0000-0002-7856-4899 surname: Pasquini fullname: Pasquini, Mirko email: mirko.pasquini16@imperial.ac.uk, pasqu@kth.se organization: Department of Electrical and Electronic Engineering, Imperial College of London, Division of Decision and Control, KTH Royal Institute of Technology, Competence Centre for Advanced Bioproduction by Continuous Processing, AdBIOPRO – sequence: 2 givenname: David surname: Angeli fullname: Angeli, David organization: Department of Electrical and Electronic Engineering, Imperial College of London, Department of Information Engineering, University of Florence |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/34792652$$D View this record in MEDLINE/PubMed https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-305663$$DView record from Swedish Publication Index |
| BookMark | eNp9kk9v3CAQxVGVqtmk_QI9VEi99OIWjA24h0pR-ldaKZeoV4RhvEviBRfwRvvty3Y3bZNDTgjm9948DXOGTnzwgNBrSt5TQsSHREgt24rUtCKUd6Riz9CCNqyuaEP5CVoQRljFJa1P0VlKN4RQ0Xb0BTpljehq3tYLFK48NsFvIa7AG8BDiHi966OzeBMsjAmHAZcS4AiredQ5xB32kO9CvE149hYinsK4y2FyptwNxKydzw7SR6zxcqen2Yct1tMUgzbrl-j5oMcEr47nObr--uX68nu1vPr24_JiWZmW1rmSghApRM1aNjBLOmptL7WwA-Oy6wCE6Uljtej00JKetV3XSwnlUVrWMMvOUXWwTXcwzb2aotvouFNBO_XZ_bxQIa7UbV4rRlrOWeE_HfgCb8Aa8Dnq8YHsYcW7tVqFrZK8jJ_LYvDuaBDDrxlSVhuXDIyj9hDmpOoSkQjBxb7X20foTZijL9PYU1IyTtqmUG_-T_Q3yv3XFUAeABNDShEGZVzW2YV9QDcqStR-S9RhS1SJqf5sidonqB9J792fFLHjSAvsVxD_xX5C9RvjjtFi |
| CitedBy_id | crossref_primary_10_1177_01423312231163926 crossref_primary_10_1007_s12064_022_00370_0 crossref_primary_10_3934_era_2023157 |
| Cites_doi | 10.1016/j.bulm.2003.08.010 10.1145/362814.362819 10.1016/j.automatica.2014.08.012 10.1109/TAC.2005.843848 10.1109/TAC.2015.2427691 10.1093/bioinformatics/btf851 10.1038/nrm2503 10.1016/0022-5193(73)90208-7 10.1016/j.physd.2012.12.006 10.1007/s002850050103 10.1109/TAC.2007.894515 10.1016/j.biosystems.2020.104113 10.1016/j.sysconle.2005.05.003 10.3934/mbe.2008.5.1 10.1007/978-94-015-7793-9 10.1016/j.jtbi.2009.06.006 10.1146/annurev-control-060117-105052 10.1038/35002131 10.1016/j.automatica.2008.01.030 10.1080/10556789908805762 10.1007/978-1-4612-0017-8 10.1109/TAC.2019.2945214 10.1016/j.biosystems.2005.10.005 10.1007/s00285-005-0338-2 10.1109/9.486646 10.1137/15M1052743 10.1038/nrg3885 10.1080/0020717031000114968 10.1109/CDC.2004.1429393 10.23919/ECC.2013.6669862 10.1109/CDC.2017.8264471 10.1109/CDC.2018.8618943 10.1109/CDC.2018.8618671 10.1142/9789812777171_0037 10.1109/CDC.2017.8264551 10.1109/CDC.1999.831273 10.1109/.2005.1466986 10.1016/j.automatica.2017.03.011 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2021 2021. The Author(s). The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2021 – notice: 2021. The Author(s). – notice: The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION CGR CUY CVF ECM EIF NPM 3V. 7TK 7TM 7U9 7X7 7XB 88A 88E 8AO 8FD 8FE 8FG 8FH 8FI 8FJ 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BBNVY BENPR BGLVJ BHPHI CCPQU DWQXO FR3 FYUFA GHDGH GNUQQ H94 HCIFZ JQ2 K7- K9. L6V LK8 M0S M1P M7N M7P M7S M7Z P5Z P62 P64 PHGZM PHGZT PJZUB PKEHL PPXIY PQEST PQGLB PQQKQ PQUKI PTHSS 7X8 5PM ADTPV AFDQA AOWAS D8T D8V ZZAVC |
| DOI | 10.1007/s00285-021-01690-3 |
| DatabaseName | Springer Nature OA Free Journals (WRLC) CrossRef Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed ProQuest Central (Corporate) Neurosciences Abstracts Nucleic Acids Abstracts Virology and AIDS Abstracts Health & Medical Collection (Proquest) ProQuest Central (purchase pre-March 2016) Biology Database (Alumni Edition) Medical Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection Hospital Premium Collection Hospital Premium Collection (Alumni Edition) ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials Biological Science Collection ProQuest Central Technology Collection Natural Science Collection ProQuest One ProQuest Central Korea Engineering Research Database Health Research Premium Collection Health Research Premium Collection (Alumni) ProQuest Central Student AIDS and Cancer Research Abstracts SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Health & Medical Complete (Alumni) ProQuest Engineering Collection ProQuest Biological Science Collection ProQuest Health & Medical Collection Medical Database Algology Mycology and Protozoology Abstracts (Microbiology C) Biological Science Database Engineering Database Biochemistry Abstracts 1 Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Biotechnology and BioEngineering Abstracts ProQuest Central Premium ProQuest One Academic (New) ProQuest Health & Medical Research Collection ProQuest One Academic Middle East (New) ProQuest One Health & Nursing ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition Engineering Collection MEDLINE - Academic PubMed Central (Full Participant titles) SwePub SWEPUB Kungliga Tekniska Högskolan full text SwePub Articles SWEPUB Freely available online SWEPUB Kungliga Tekniska Högskolan SwePub Articles full text |
| DatabaseTitle | CrossRef MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Nucleic Acids Abstracts SciTech Premium Collection ProQuest One Applied & Life Sciences Health Research Premium Collection Natural Science Collection Health & Medical Research Collection Biological Science Collection ProQuest Central (New) ProQuest Medical Library (Alumni) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database Virology and AIDS Abstracts ProQuest Biological Science Collection ProQuest One Academic Eastern Edition ProQuest Hospital Collection ProQuest Technology Collection Health Research Premium Collection (Alumni) Biological Science Database Neurosciences Abstracts ProQuest Hospital Collection (Alumni) Biotechnology and BioEngineering Abstracts ProQuest Health & Medical Complete ProQuest One Academic UKI Edition Engineering Research Database ProQuest One Academic ProQuest One Academic (New) Technology Collection Technology Research Database ProQuest One Academic Middle East (New) ProQuest Health & Medical Complete (Alumni) ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest One Health & Nursing ProQuest Natural Science Collection ProQuest Pharma Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ProQuest Health & Medical Research Collection ProQuest Engineering Collection Health and Medicine Complete (Alumni Edition) ProQuest Central Korea Algology Mycology and Protozoology Abstracts (Microbiology C) AIDS and Cancer Research Abstracts ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest Medical Library Materials Science & Engineering Collection Biochemistry Abstracts 1 ProQuest Central (Alumni) MEDLINE - Academic |
| DatabaseTitleList | Computer Science Database MEDLINE CrossRef MEDLINE - Academic |
| Database_xml | – sequence: 1 dbid: C6C name: Springer Nature OA Free Journals (WRLC) url: http://www.springeropen.com/ sourceTypes: Publisher – sequence: 2 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 3 dbid: EIF name: MEDLINE url: https://proxy.k.utb.cz/login?url=https://www.webofscience.com/wos/medline/basic-search sourceTypes: Index Database – sequence: 4 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Biology Mathematics Engineering |
| EISSN | 1432-1416 |
| ExternalDocumentID | oai_DiVA_org_kth_305663 PMC8602168 34792652 10_1007_s00285_021_01690_3 |
| Genre | Research Support, Non-U.S. Gov't Journal Article |
| GrantInformation_xml | – fundername: Engineering and Physical Sciences Research Council grantid: 1895642 funderid: http://dx.doi.org/10.13039/501100000266 – fundername: Department of Electrical and Electronic Engineering, Imperial College of London – fundername: ; – fundername: ; grantid: 1895642 |
| GroupedDBID | --- -52 -5D -5G -BR -EM -Y2 -~C -~X .86 06D 0R~ 0VY 186 199 1N0 1SB 2.D 203 28- 29L 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 3-Y 30V 3SX 3V. 4.4 406 408 409 40D 40E 53G 5GY 5QI 5VS 67Z 6NX 78A 7X7 88A 88E 8AO 8FE 8FG 8FH 8FI 8FJ 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAGAY AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACPRK ACZOJ ADBBV ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFRAH AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHMBA AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALIPV ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBNVY BBWZM BDATZ BENPR BGLVJ BGNMA BHPHI BPHCQ BSONS BVXVI C6C CAG CCPQU COF CS3 CSCUP D0L DDRTE DL5 DNIVK DPUIP DU5 EBD EBLON EBS EIOEI EJD EMB EMOBN EPAXT ESBYG F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC FYUFA GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMCUK HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K6V K7- KDC KOV KOW L6V LAS LK8 LLZTM M0L M1P M4Y M7P M7S MA- MQGED MVM N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQQKQ PROAC PSQYO PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RRX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SV3 SZN T13 T16 TN5 TSG TSK TSV TUC U2A U9L UG4 UKHRP UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WIP WJK WK6 WK8 YLTOR YQT Z45 Z7U ZMTXR ZWQNP ZXP ~EX ~KM AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT CGR CUY CVF ECM EIF NPM 7TK 7TM 7U9 7XB 8FD 8FK ABRTQ AZQEC DWQXO FR3 GNUQQ H94 JQ2 K9. M7N M7Z P64 PJZUB PKEHL PPXIY PQEST PQGLB PQUKI 7X8 5PM ADTPV AFDQA AOWAS D8T D8V ZZAVC |
| ID | FETCH-LOGICAL-c512t-87008772353f3d091ddb8a7df36899ee7cb04da79af50b3599b88ecb08d343d3 |
| IEDL.DBID | U2A |
| ISSN | 0303-6812 1432-1416 |
| IngestDate | Thu Aug 21 06:49:39 EDT 2025 Thu Aug 21 14:09:27 EDT 2025 Thu Jul 10 19:55:08 EDT 2025 Fri Jul 25 19:03:25 EDT 2025 Wed Feb 19 02:27:35 EST 2025 Thu Apr 24 22:59:30 EDT 2025 Tue Jul 01 02:03:16 EDT 2025 Fri Feb 21 02:47:26 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6-7 |
| Keywords | Gene regulatory networks 92C42 Systems biology Linear matrix inequalities 93D30 Lyapunov methods Convergence analysis Polytopic uncertainties |
| Language | English |
| License | 2021. The Author(s). Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c512t-87008772353f3d091ddb8a7df36899ee7cb04da79af50b3599b88ecb08d343d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| ORCID | 0000-0002-7856-4899 |
| OpenAccessLink | https://link.springer.com/10.1007/s00285-021-01690-3 |
| PMID | 34792652 |
| PQID | 2598836054 |
| PQPubID | 54026 |
| ParticipantIDs | swepub_primary_oai_DiVA_org_kth_305663 pubmedcentral_primary_oai_pubmedcentral_nih_gov_8602168 proquest_miscellaneous_2599077673 proquest_journals_2598836054 pubmed_primary_34792652 crossref_citationtrail_10_1007_s00285_021_01690_3 crossref_primary_10_1007_s00285_021_01690_3 springer_journals_10_1007_s00285_021_01690_3 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2021-12-01 |
| PublicationDateYYYYMMDD | 2021-12-01 |
| PublicationDate_xml | – month: 12 year: 2021 text: 2021-12-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Germany – name: Heidelberg |
| PublicationTitle | Journal of mathematical biology |
| PublicationTitleAbbrev | J. Math. Biol |
| PublicationTitleAlternate | J Math Biol |
| PublicationYear | 2021 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Alon (CR2) 2007 Filippov (CR15) 1988 Qian, McBride, Del Vecchio (CR38) 2018; 1 Ropers, de Jong, Page, Schneider, Geiselmann (CR39) 2006; 84 Gahinet, Apkarian, Chilali (CR18) 1996; 41 Zhai, Lin, Antsaklis (CR45) 2003; 76 CR16 Oliveira, Peres (CR34) 2006; 55 Glass, Kauffman (CR20) 1973; 39 CR35 De Jong, Gouzé, Hernandez, Page, Sari, Geiselmann (CR14) 2004; 66 CR33 Wang, Wang (CR44) 2013; 246 CR31 Plahte, Mestl, Omholt (CR37) 1998; 36 De Jong, Geiselmann, Hernandez, Page (CR13) 2003; 19 Khalil (CR26) 2002 Liberzon (CR28) 2003 Le Novère (CR27) 2015; 16 Saadatpour, Albert (CR40) 2016; 4 Ali Al-Radhawi, Angeli (CR1) 2016; 61 CR4 Murray, Del Vecchio (CR32) 2014 CR6 Toh, Todd, Tütüncü (CR42) 1999; 11 CR29 CR9 Grognard, de Jong, Gouzé (CR21) 2007 CR24 Collins, Gardner, Cantor (CR11) 2000; 403 CR23 CR22 Pasquini, Angeli (CR36) 2019; 65 Cummins, Gedeon, Harker, Mischaikow, Mok (CR12) 2016; 15 Lin, Antsaklis (CR30) 2007; 52 Chesi, Garulli, Tesi, Vicino (CR10) 2005; 50 Gedeon (CR19) 2020; 190 Freeman (CR17) 2014 Chesi, Hung (CR8) 2008; 44 Tournier, Chaves (CR43) 2009; 260 Blanchini, Giordano (CR5) 2014; 50 Tiernan (CR41) 1970; 13 Arcak, Sontag (CR3) 2008; 5 Casey, De Jong, Gouzé (CR7) 2006; 52 Karlebach, Shamir (CR25) 2008; 9 G Karlebach (1690_CR25) 2008; 9 RCLF Oliveira (1690_CR34) 2006; 55 U Alon (1690_CR2) 2007 M Pasquini (1690_CR36) 2019; 65 F Blanchini (1690_CR5) 2014; 50 R Casey (1690_CR7) 2006; 52 1690_CR29 N Le Novère (1690_CR27) 2015; 16 1690_CR24 D Liberzon (1690_CR28) 2003 1690_CR22 1690_CR23 E Plahte (1690_CR37) 1998; 36 G Chesi (1690_CR10) 2005; 50 F Grognard (1690_CR21) 2007 G Chesi (1690_CR8) 2008; 44 JC Tiernan (1690_CR41) 1970; 13 H De Jong (1690_CR13) 2003; 19 1690_CR9 1690_CR6 P Gahinet (1690_CR18) 1996; 41 1690_CR4 T Gedeon (1690_CR19) 2020; 190 M Arcak (1690_CR3) 2008; 5 JJ Collins (1690_CR11) 2000; 403 D Ropers (1690_CR39) 2006; 84 1690_CR16 K-C Toh (1690_CR42) 1999; 11 1690_CR35 H De Jong (1690_CR14) 2004; 66 B Cummins (1690_CR12) 2016; 15 1690_CR33 J Wang (1690_CR44) 2013; 246 L Tournier (1690_CR43) 2009; 260 1690_CR31 M Ali Al-Radhawi (1690_CR1) 2016; 61 L Glass (1690_CR20) 1973; 39 AF Filippov (1690_CR15) 1988 S Freeman (1690_CR17) 2014 H Lin (1690_CR30) 2007; 52 A Saadatpour (1690_CR40) 2016; 4 HK Khalil (1690_CR26) 2002 Y Qian (1690_CR38) 2018; 1 RM Murray (1690_CR32) 2014 G Zhai (1690_CR45) 2003; 76 |
| References_xml | – year: 2007 ident: CR2 publication-title: An introduction to systems biology: design principles of biological circuits – ident: CR22 – volume: 66 start-page: 301 issue: 2 year: 2004 end-page: 340 ident: CR14 article-title: Qualitative simulation of genetic regulatory networks using piecewise-linear models publication-title: Bull Math Biol doi: 10.1016/j.bulm.2003.08.010 – volume: 13 start-page: 722 issue: 12 year: 1970 end-page: 726 ident: CR41 article-title: An efficient search algorithm to find the elementary circuits of a graph publication-title: Commun ACM doi: 10.1145/362814.362819 – volume: 50 start-page: 2482 issue: 10 year: 2014 end-page: 2493 ident: CR5 article-title: Piecewise-linear Lyapunov functions for structural stability of biochemical networks publication-title: Automatica doi: 10.1016/j.automatica.2014.08.012 – volume: 50 start-page: 365 issue: 3 year: 2005 end-page: 370 ident: CR10 article-title: Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2005.843848 – volume: 61 start-page: 76 issue: 1 year: 2016 end-page: 89 ident: CR1 article-title: New approach to the stability of chemical reaction networks: piecewise linear in rates Lyapunov functions publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2015.2427691 – volume: 19 start-page: 336 issue: 3 year: 2003 end-page: 344 ident: CR13 article-title: Genetic network analyzer: qualitative simulation of genetic regulatory networks publication-title: Bioinformatics doi: 10.1093/bioinformatics/btf851 – ident: CR4 – volume: 9 start-page: 770 issue: 10 year: 2008 end-page: 780 ident: CR25 article-title: Modelling and analysis of gene regulatory networks publication-title: Nat Rev Mol Cell Biol doi: 10.1038/nrm2503 – ident: CR16 – volume: 39 start-page: 103 issue: 1 year: 1973 end-page: 129 ident: CR20 article-title: The logical analysis of continuous, non-linear biochemical control networks publication-title: J Theor Biol doi: 10.1016/0022-5193(73)90208-7 – volume: 246 start-page: 39 issue: 1 year: 2013 end-page: 49 ident: CR44 article-title: State transition graph and stability of singular equilibria for piecewise linear biological models publication-title: Physica D Nonlinear Phenom doi: 10.1016/j.physd.2012.12.006 – volume: 36 start-page: 321 issue: 4 year: 1998 end-page: 348 ident: CR37 article-title: A methodological basis for description and analysis of systems with complex switch-like interactions publication-title: J Math Biol doi: 10.1007/s002850050103 – volume: 52 start-page: 633 issue: 4 year: 2007 end-page: 646 ident: CR30 article-title: Switching stabilizability for continuous-time uncertain switched linear systems publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2007.894515 – ident: CR33 – volume: 190 start-page: 104113 year: 2020 ident: CR19 article-title: Multi-parameter exploration of dynamics of regulatory networks publication-title: Biosystems doi: 10.1016/j.biosystems.2020.104113 – ident: CR35 – ident: CR6 – ident: CR29 – volume: 55 start-page: 52 issue: 1 year: 2006 end-page: 61 ident: CR34 article-title: LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions publication-title: Syst Control Lett doi: 10.1016/j.sysconle.2005.05.003 – start-page: 137 year: 2007 end-page: 159 ident: CR21 publication-title: Piecewise-linear models of genetic regulatory networks: theory and example – year: 2014 ident: CR32 publication-title: Biomolecular feedback systems – volume: 5 start-page: 1 issue: 1 year: 2008 ident: CR3 article-title: A passivity-based stability criterion for a class of biochemical reaction networks publication-title: Math Biosci Eng doi: 10.3934/mbe.2008.5.1 – ident: CR23 – volume: 4 start-page: 1 issue: 5 year: 2016 end-page: 13 ident: CR40 article-title: A comparative study of qualitative and quantitative dynamic models of biological regulatory networks publication-title: EPJ Nonlinear Biomed Phys – year: 2002 ident: CR26 publication-title: Nonlinear systems – year: 2014 ident: CR17 publication-title: Biological science – year: 1988 ident: CR15 publication-title: Differential equations with discontinuous righthand sides doi: 10.1007/978-94-015-7793-9 – ident: CR31 – volume: 260 start-page: 196 issue: 2 year: 2009 end-page: 209 ident: CR43 article-title: Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics publication-title: J Theor Biol doi: 10.1016/j.jtbi.2009.06.006 – volume: 1 start-page: 411 issue: 1 year: 2018 end-page: 440 ident: CR38 article-title: Programming cells to work for us publication-title: Annu Rev Control Robot Autonom Syst doi: 10.1146/annurev-control-060117-105052 – ident: CR9 – volume: 403 start-page: 339 year: 2000 end-page: 342 ident: CR11 article-title: Construction of a genetic toggle switch in publication-title: Nature doi: 10.1038/35002131 – volume: 44 start-page: 2298 issue: 9 year: 2008 end-page: 2305 ident: CR8 article-title: Stability analysis of uncertain genetic sum regulatory networks publication-title: Automatica doi: 10.1016/j.automatica.2008.01.030 – volume: 11 start-page: 545 issue: 1–4 year: 1999 end-page: 581 ident: CR42 article-title: Sdpt3-a MATLAB software package for semidefinite programming, version 1.3 publication-title: Optim Methods Softw doi: 10.1080/10556789908805762 – year: 2003 ident: CR28 publication-title: Switching in systems and control doi: 10.1007/978-1-4612-0017-8 – volume: 65 start-page: 3333 year: 2019 end-page: 3348 ident: CR36 article-title: On convergence for piecewise affine models of gene regulatory networks via a Lyapunov approach publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2019.2945214 – volume: 84 start-page: 124 issue: 2 year: 2006 end-page: 152 ident: CR39 article-title: Qualitative simulation of the carbon starvation response in publication-title: BioSystems doi: 10.1016/j.biosystems.2005.10.005 – volume: 52 start-page: 27 issue: 1 year: 2006 end-page: 56 ident: CR7 article-title: Piecewise-linear models of genetic regulatory networks: equilibria and their stability publication-title: J Math Biol doi: 10.1007/s00285-005-0338-2 – volume: 41 start-page: 436 issue: 3 year: 1996 end-page: 442 ident: CR18 article-title: Affine parameter-dependent Lyapunov functions and real parametric uncertainty publication-title: IEEE Trans Autom Control doi: 10.1109/9.486646 – volume: 15 start-page: 2176 issue: 4 year: 2016 end-page: 2212 ident: CR12 article-title: Combinatorial representation of parameter space for switching networks publication-title: SIAM J Appl Dyn Syst doi: 10.1137/15M1052743 – ident: CR24 – volume: 16 start-page: 146 issue: 3 year: 2015 end-page: 58 ident: CR27 article-title: Quantitative and logic modelling of molecular and gene networks publication-title: Nat Rev Genet doi: 10.1038/nrg3885 – volume: 76 start-page: 747 issue: 7 year: 2003 end-page: 753 ident: CR45 article-title: Quadratic stabilizability of switched linear systems with polytopic uncertainties publication-title: Int J Control doi: 10.1080/0020717031000114968 – start-page: 137 volume-title: Piecewise-linear models of genetic regulatory networks: theory and example year: 2007 ident: 1690_CR21 – volume: 5 start-page: 1 issue: 1 year: 2008 ident: 1690_CR3 publication-title: Math Biosci Eng doi: 10.3934/mbe.2008.5.1 – volume: 36 start-page: 321 issue: 4 year: 1998 ident: 1690_CR37 publication-title: J Math Biol doi: 10.1007/s002850050103 – volume: 52 start-page: 633 issue: 4 year: 2007 ident: 1690_CR30 publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2007.894515 – volume: 4 start-page: 1 issue: 5 year: 2016 ident: 1690_CR40 publication-title: EPJ Nonlinear Biomed Phys – volume: 15 start-page: 2176 issue: 4 year: 2016 ident: 1690_CR12 publication-title: SIAM J Appl Dyn Syst doi: 10.1137/15M1052743 – ident: 1690_CR9 doi: 10.1109/CDC.2004.1429393 – volume: 403 start-page: 339 year: 2000 ident: 1690_CR11 publication-title: Nature doi: 10.1038/35002131 – volume: 50 start-page: 365 issue: 3 year: 2005 ident: 1690_CR10 publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2005.843848 – volume-title: Biological science year: 2014 ident: 1690_CR17 – ident: 1690_CR22 doi: 10.23919/ECC.2013.6669862 – volume: 39 start-page: 103 issue: 1 year: 1973 ident: 1690_CR20 publication-title: J Theor Biol doi: 10.1016/0022-5193(73)90208-7 – volume: 44 start-page: 2298 issue: 9 year: 2008 ident: 1690_CR8 publication-title: Automatica doi: 10.1016/j.automatica.2008.01.030 – ident: 1690_CR31 – volume: 65 start-page: 3333 year: 2019 ident: 1690_CR36 publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2019.2945214 – volume-title: Differential equations with discontinuous righthand sides year: 1988 ident: 1690_CR15 doi: 10.1007/978-94-015-7793-9 – volume: 16 start-page: 146 issue: 3 year: 2015 ident: 1690_CR27 publication-title: Nat Rev Genet doi: 10.1038/nrg3885 – volume: 260 start-page: 196 issue: 2 year: 2009 ident: 1690_CR43 publication-title: J Theor Biol doi: 10.1016/j.jtbi.2009.06.006 – ident: 1690_CR16 doi: 10.1109/CDC.2017.8264471 – volume: 13 start-page: 722 issue: 12 year: 1970 ident: 1690_CR41 publication-title: Commun ACM doi: 10.1145/362814.362819 – ident: 1690_CR6 doi: 10.1109/CDC.2018.8618943 – volume: 52 start-page: 27 issue: 1 year: 2006 ident: 1690_CR7 publication-title: J Math Biol doi: 10.1007/s00285-005-0338-2 – volume: 55 start-page: 52 issue: 1 year: 2006 ident: 1690_CR34 publication-title: Syst Control Lett doi: 10.1016/j.sysconle.2005.05.003 – volume: 41 start-page: 436 issue: 3 year: 1996 ident: 1690_CR18 publication-title: IEEE Trans Autom Control doi: 10.1109/9.486646 – volume-title: Nonlinear systems year: 2002 ident: 1690_CR26 – volume: 1 start-page: 411 issue: 1 year: 2018 ident: 1690_CR38 publication-title: Annu Rev Control Robot Autonom Syst doi: 10.1146/annurev-control-060117-105052 – volume: 61 start-page: 76 issue: 1 year: 2016 ident: 1690_CR1 publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2015.2427691 – ident: 1690_CR35 doi: 10.1109/CDC.2018.8618671 – volume: 84 start-page: 124 issue: 2 year: 2006 ident: 1690_CR39 publication-title: BioSystems doi: 10.1016/j.biosystems.2005.10.005 – volume: 19 start-page: 336 issue: 3 year: 2003 ident: 1690_CR13 publication-title: Bioinformatics doi: 10.1093/bioinformatics/btf851 – ident: 1690_CR4 doi: 10.1142/9789812777171_0037 – volume: 76 start-page: 747 issue: 7 year: 2003 ident: 1690_CR45 publication-title: Int J Control doi: 10.1080/0020717031000114968 – volume: 66 start-page: 301 issue: 2 year: 2004 ident: 1690_CR14 publication-title: Bull Math Biol doi: 10.1016/j.bulm.2003.08.010 – ident: 1690_CR24 doi: 10.1109/CDC.2017.8264551 – volume: 246 start-page: 39 issue: 1 year: 2013 ident: 1690_CR44 publication-title: Physica D Nonlinear Phenom doi: 10.1016/j.physd.2012.12.006 – volume: 9 start-page: 770 issue: 10 year: 2008 ident: 1690_CR25 publication-title: Nat Rev Mol Cell Biol doi: 10.1038/nrm2503 – volume-title: An introduction to systems biology: design principles of biological circuits year: 2007 ident: 1690_CR2 – ident: 1690_CR33 doi: 10.1109/CDC.1999.831273 – volume-title: Switching in systems and control year: 2003 ident: 1690_CR28 doi: 10.1007/978-1-4612-0017-8 – ident: 1690_CR29 doi: 10.1109/.2005.1466986 – volume: 190 start-page: 104113 year: 2020 ident: 1690_CR19 publication-title: Biosystems doi: 10.1016/j.biosystems.2020.104113 – volume-title: Biomolecular feedback systems year: 2014 ident: 1690_CR32 – ident: 1690_CR23 doi: 10.1016/j.automatica.2017.03.011 – volume: 11 start-page: 545 issue: 1–4 year: 1999 ident: 1690_CR42 publication-title: Optim Methods Softw doi: 10.1080/10556789908805762 – volume: 50 start-page: 2482 issue: 10 year: 2014 ident: 1690_CR5 publication-title: Automatica doi: 10.1016/j.automatica.2014.08.012 |
| SSID | ssj0017591 |
| Score | 2.3399348 |
| Snippet | Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main... |
| SourceID | swepub pubmedcentral proquest pubmed crossref springer |
| SourceType | Open Access Repository Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 64 |
| SubjectTerms | Applications of Mathematics Approximation Biology Chemical reactions Control theory Convergence Convergence analysis Engineering Gene Regulatory Networks Genes Liapunov functions Linear matrix inequalities Lyapunov methods Mathematical and Computational Biology Mathematical models Mathematics Mathematics and Statistics Parameters Polytopic uncertainties Systems biology Systems stability Transcription factors Uncertainty |
| SummonAdditionalLinks | – databaseName: Health & Medical Collection (Proquest) dbid: 7X7 link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1Lb9QwEB5BERIcEJTXQkFGQlwgohvn4XBBFVBViMeloL1Zju10V1Rxms1Wyr9nxk5Slkp7zNp57YznEc98H8BrQ1A-qioiYWOiMBM2wjwkj9DTKz03hba-y_X7j-zkV_J1kS6GD27roaxytIneUBun6Rv5ewzTBTUcpMnH5iIi1ijaXR0oNG7CLYIuo5KufDElXOgZA2MemumIcLaGphnfOkfJBvUmUzKNGWLEtx3TtWjzetHktHP6H8qo90zH9-HeEFKyo6ADD-CGrffhdiCZ7Pfh7j-Qgw_B_ayZrzT3TZeWYczKlj21bTFPirNmrmI4ZFkbWOpd27M61IqvGXWctaxx533nmpXGYx1KCgiW9QNT7Fuvmk3tLtmIVf4ITo-_nH46iQbShUij7-_QOhJKXR7zlFfcYDRhTClUbiqeYWpmba7Lw8SovFBVeljytChKISz-KAxPuOGPYa92tX0KTKfKCDSfXGUqMRZPrlALitKmquI2jmcwH_9wqQdAcuLFOJcTlLIXkkQhSS8kyWfwdjqnCXAcO2cfjHKUw9JcyytFmsGraRgXFe2UqNq6jZ9TeJwjvMSTIPbpdtR6G2cpPn6-pRDTBALs3h6pV0sP3E18X_NMzODdqDpXj7XrLd4E9dq6w-fV7yPp2jP5p1tKygMz_mz36z6HOzHpu6_FOYC9rt3YFxhRdeVLv2z-At1SHrc priority: 102 providerName: ProQuest |
| Title | On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach |
| URI | https://link.springer.com/article/10.1007/s00285-021-01690-3 https://www.ncbi.nlm.nih.gov/pubmed/34792652 https://www.proquest.com/docview/2598836054 https://www.proquest.com/docview/2599077673 https://pubmed.ncbi.nlm.nih.gov/PMC8602168 https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-305663 |
| Volume | 83 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fb9MwED6xTUjwMMGA0TEqIyFeINIax4nDWyntJmADoQ2VJ8uJHVoxJVWTIuW_5875gcrQJF4SJXbsJHe27-T7vgN4aYjKR2exJ61PKcyk9dAPiTxc6XU6MnFqHcr1_CI8uwo-zMW8BYWVXbR7tyXpZuoe7EbuAaGJyf1Fn87jO7AnyHdHLb7yx_3eQSSaPHk4OXvErtVCZf7dxvZydMPGvBkq2e-X_sUt6taj2QPYbw1JNm4k_xDu2PwA7japJesDuH_e87GWj6D4nDMXX-6glpahpcoWNYG1mEuFU7IiY1hk2brJTV-sa5Y3EeIlI5zZmq2K67oqVssUr9MmkIDIWN8yzT7VerXJi1-sYyh_DJez6eXkzGtTLXgprvgVzonETRf5XPCMG7QhjEmkjkzGQ3TIrI3S5CQwOop1Jk4SLuI4kdLiTWl4wA1_Art5kdunwFKhjcRJk-tQB8biwxnKPk6s0Bm3vj-AUffDVdrSkFM2jGvVEyg7ISkUknJCUnwAr_tnVg0Jx621jzs5qnZAlgq9PEl4FREM4EVfjEOJ9kd0bouNqxM7diNs4rARe98dAW79UODrR1sK0Vcgmu7tkny5cHTdlOVrFMoBvOlU589r3fYVrxr12urh_fLbWBXrH-pntVDk_YX86P_afQb3fNJ_F5FzDLvVemOfo11VJUPYieYRHuXsdAh749PvH6d4fje9-PIV707CydANtN8pJCFb |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEB6VIgQcEJRHAwUWCbiAReP1EwmhihJSmpZLQL2t1t51E7XyGscB-UfxH5lZP0qolFuP9q5fmZmdmezM9wG8VATlI7PYibRLFGaRdjAPCR309DIdqjjVtsv16DgYf_e-nvgnG_Cn64WhsspuTbQLtTIp_Uf-DsP0iBoOfO9j8dMh1ijaXe0oNBq1ONT1b0zZFh8O9lG-r1x39Hn6aey0rAJOis6tQvMnGLbQ5T7PuEJ3qVQSyVBlPMDcQ-swTXY9JcNYZv5uwv04TqJI48lIcY8rjre9Btc9zmMyqGj0pd-0CP2GoA-9gkOwXm2Pju3Uo9yGWqEpd8eE1OGrfvBScHu5RrPfqP0P1NQ6wtFduNNGsGyvUbl7sKHzLbjRcFrWW3D7H4TD-2C-5cwWttseT80wRGazmrrEmOXgWTCTMRzSrNSnxCRmyprlTWn6glGDW8kKc15XppineJw2FQyEAvueSTapZbHMzS_WQaM_gOlVSOMhbOYm19vAUl-qCFdrLgPpKY0XZ6h0caJ9mXHtugMYdj-4SFv8c6LhOBc9crMVkkAhCSskwQfwpr-maNA_1s7e6eQo2pVgIS70dgAv-mG0YdqYkbk2SzsntrBKeItHjdj7x1Gnrxv4-PrhikL0EwgffHUkn88sTjjRiw2DaABvO9W5eK11X_G6Ua-VJ-zPf-wJU56Ks2omKO0M-OP1n_scbo6nRxMxOTg-fAK3XNJ9Wwa0A5tVudRPMZirkmfWhBiIKzbZv45KWsU |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEB6VIhAcKiiv0AKLBFzAauP1s1KFKkLU0lI4FJTbau1dNxGV1zgOyD-Nf8fM-lFCpdx6tHf9yszszGRnvg_glSIoH5nFTqRdojCLtIN5SOigp5fpUMWptl2un0-Dw2_ep4k_WYM_XS8MlVV2a6JdqJVJ6T_yHQzTI2o48L2drC2L-Doavy9-OsQgRTutHZ1GoyLHuv6N6dt8_2iEsn7tuuOPZx8OnZZhwEnR0VW4FBAkW-hyn2dcoetUKolkqDIeYB6idZgmu56SYSwzfzfhfhwnUaTxZKS4xxXH296AmyH3h2Ri4aTP9dApN2R96CEcgvhq-3Vs1x7lOdQWTXk8JqcOX_aJVwLdq_Wa_abtfwCn1imO78FGG82yg0b97sOazjfhVsNvWW_C3X_QDh-A-ZIzW-Ru-z01w3CZTWvqGGOWj2fOTMZwSLNSnxOrmClrljdl6nNGzW4lK8xFXZliluJx2lQzECLsHpPspJbFIje_WAeT_hDOrkMaj2A9N7l-Aiz1pYpw5eYykJ7SeHGGChgn2pcZ1647gGH3g4u0xUInSo4L0aM4WyEJFJKwQhJ8AG_7a4oGCWTl7O1OjqJdFebiUocH8LIfRnumTRqZa7Owc2ILsYS3eNyIvX8cdf26gY-vHy4pRD-BsMKXR_LZ1GKGE9XYMIgG8K5TncvXWvUVbxr1WnrCaPb9QJjyXPyopoJS0IA_Xf25L-A2Gqs4OTo93oI7Lqm-rQjahvWqXOhnGNdVyXNrQQzENVvsX568XvI |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+convergence+for+hybrid+models+of+gene+regulatory+networks+under+polytopic+uncertainties%3A+a+Lyapunov+approach&rft.jtitle=Journal+of+mathematical+biology&rft.au=Pasquini%2C+Mirko&rft.au=Angeli%2C+David&rft.date=2021-12-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0303-6812&rft.eissn=1432-1416&rft.volume=83&rft.issue=6-7&rft_id=info:doi/10.1007%2Fs00285-021-01690-3&rft_id=info%3Apmid%2F34792652&rft.externalDocID=PMC8602168 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0303-6812&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0303-6812&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0303-6812&client=summon |