The effect of inhibitor on the plasmid-bearing and plasmid-free model in the unstirred chemostat
This paper deals with a chemostat model with an inhibitor in the context of competition between plasmid-bearing and plasmid-free organisms. First, sufficient conditions for coexistence of the steady-state are determined. Second, the effects of the inhibitor are considered. It turns out that the para...
Saved in:
Published in | SIAM journal on mathematical analysis Vol. 38; no. 6; pp. 1860 - 1885 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
2007
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | This paper deals with a chemostat model with an inhibitor in the context of competition between plasmid-bearing and plasmid-free organisms. First, sufficient conditions for coexistence of the steady-state are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter μ, which represents the effect of the inhibitor, plays a very important role in deciding the number of the coexistence solutions. The results show that if μ is sufficiently large this model has at least two coexistence solutions provided that the maximal growth rate $a$ of $u$ lies in a certain range and has only one unique asymptotically stable coexistence solution when $a$ belongs to another range. Finally, extensive simulations are done to complement the analytic results. The main tools used here include degree theory in cones, bifurcation theory, and perturbation technique. |
---|---|
AbstractList | This paper deals with a chemostat model with an inhibitor in the context of competition between plasmid-bearing and plasmid-free organisms. First, sufficient conditions for coexistence of the steady-state are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter μ, which represents the effect of the inhibitor, plays a very important role in deciding the number of the coexistence solutions. The results show that if μ is sufficiently large this model has at least two coexistence solutions provided that the maximal growth rate $a$ of $u$ lies in a certain range and has only one unique asymptotically stable coexistence solution when $a$ belongs to another range. Finally, extensive simulations are done to complement the analytic results. The main tools used here include degree theory in cones, bifurcation theory, and perturbation technique. |
Author | WOLKOWICZ, Gail S. K HUA NIE JIANHUA WU |
Author_xml | – sequence: 1 surname: JIANHUA WU fullname: JIANHUA WU organization: College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China – sequence: 2 surname: HUA NIE fullname: HUA NIE organization: College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, China – sequence: 3 givenname: Gail S. K surname: WOLKOWICZ fullname: WOLKOWICZ, Gail S. K organization: Department of Mathematics and Statistics, McMaster University, Hamilton L8S 4K1, ON, Canada |
BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19203566$$DView record in Pascal Francis |
BookMark | eNpFkEtLAzEUhYNUsK0u_AeD4MLFaJ6TmaUUX1BwU9djHjc2pZPUJF347x2t1NXl3vudc-DM0CTEAAhdEnxLCJN3WOCGSkH4CZoS3IlaEsEnaIoxa2rCCT5Ds5w3GJOGd3iK3ldrqMA5MKWKrvJh7bUvMVUxVGV87bYqD97WGlTy4aNSwR5vLgFUQ7SwHXW_9D7k4lMCW5k1DDEXVc7RqVPbDBd_c47eHh9Wi-d6-fr0srhf1oZRUuqulZxKEJK2uqMcnFHUCEoZl0pbo6SgRqtxB-0U461uNcat7ShTYIWwbI6uDr67FD_3kEu_ifsUxsh-hDoqGMEjdHOATIo5J3D9LvlBpa-e4P6nv_7Y38he_xmqbNTWJRWMz_-CjmImmoZ9AxwfcJ0 |
CitedBy_id | crossref_primary_10_1186_s13660_016_1241_7 crossref_primary_10_1016_j_chaos_2023_113417 crossref_primary_10_1016_j_nonrwa_2012_01_006 crossref_primary_10_1080_00036811_2012_683786 crossref_primary_10_1007_s11464_009_0031_7 crossref_primary_10_3934_dcds_2012_32_303 crossref_primary_10_11948_20210452 crossref_primary_10_3934_cpaa_2013_12_1279 crossref_primary_10_1016_j_jmaa_2009_01_045 crossref_primary_10_1016_j_mbs_2019_03_001 crossref_primary_10_1002_mana_201900033 crossref_primary_10_1111_sapm_12384 crossref_primary_10_1016_j_nonrwa_2014_04_002 crossref_primary_10_1007_s10884_019_09763_0 crossref_primary_10_1063_5_0054708 crossref_primary_10_11650_tjm_20_2016_5482 crossref_primary_10_3934_dcdsb_2011_15_893 crossref_primary_10_3934_dcdsb_2015_20_2691 crossref_primary_10_1080_00036811_2016_1171319 crossref_primary_10_1080_00986445_2011_651185 crossref_primary_10_1016_j_chaos_2024_114901 crossref_primary_10_1016_j_nonrwa_2007_01_018 crossref_primary_10_3934_cpaa_2017066 crossref_primary_10_1017_prm_2020_12 crossref_primary_10_3934_dcdsb_2016_21_621 crossref_primary_10_1016_j_nonrwa_2010_01_010 crossref_primary_10_1007_s11425_012_4550_4 crossref_primary_10_1016_j_nonrwa_2019_103044 crossref_primary_10_1080_00036811_2018_1460811 crossref_primary_10_1016_j_cnsns_2024_107902 crossref_primary_10_1016_j_jmaa_2019_123724 crossref_primary_10_1186_s13662_018_1587_x crossref_primary_10_1002_mma_7376 crossref_primary_10_1155_2009_204632 crossref_primary_10_1142_S1793524519500657 crossref_primary_10_1080_00036811003717954 crossref_primary_10_1080_00036811_2024_2341789 crossref_primary_10_1016_j_jde_2009_12_014 crossref_primary_10_1016_j_nonrwa_2024_104125 crossref_primary_10_3934_dcdsb_2017128 crossref_primary_10_1017_S0956792514000096 |
Cites_doi | 10.1016/S0009-2509(96)00385-5 10.1016/S0022-5193(86)80226-0 10.1080/03605309208820844 10.1002/bit.260260819 10.1016/0009-2509(88)87125-2 10.1090/S0002-9947-97-01842-4 10.1137/0153051 10.1126/science.7268409 10.1007/BF00163028 10.1017/S0308210500023064 10.1098/rstb.1988.0059 10.1073/pnas.78.10.6324 10.1137/0152029 10.1016/0022-1236(71)90015-2 10.1007/BF00282325 10.1007/BF00180136 10.1016/S0096-3003(02)00732-4 10.1007/BF00178774 10.1016/j.mbs.2003.07.004 10.1142/S0218127406015246 10.1016/S0362-546X(98)00163-1 10.1007/BF00163024 10.1016/S0025-5564(97)10010-4 10.1137/S0036139903423285 10.1006/jdeq.2000.3870 10.1016/0022-247X(83)90098-7 10.1006/jdeq.1996.0132 |
ContentType | Journal Article |
Copyright | 2008 INIST-CNRS [Copyright] © 2007 Society for Industrial and Applied Mathematics |
Copyright_xml | – notice: 2008 INIST-CNRS – notice: [Copyright] © 2007 Society for Industrial and Applied Mathematics |
DBID | IQODW AAYXX CITATION 3V. 7RQ 7WY 7WZ 7X2 7XB 87Z 88A 88F 88I 88K 8AL 8FE 8FG 8FH 8FK 8FL 8G5 ABJCF ABUWG AFKRA ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI CCPQU D1I DWQXO FRNLG F~G GNUQQ GUQSH HCIFZ JQ2 K60 K6~ K7- KB. L.- L6V LK8 M0C M0K M0N M1Q M2O M2P M2T M7P M7S MBDVC P5Z P62 PATMY PDBOC PQBIZ PQBZA PQEST PQQKQ PQUKI PRINS PTHSS PYCSY Q9U U9A |
DOI | 10.1137/050627514 |
DatabaseName | Pascal-Francis CrossRef ProQuest Central (Corporate) ProQuest Career & Technical Education Database ProQuest_ABI/INFORM Collection ABI/INFORM Global (PDF only) Agricultural Science Collection ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Biology Database (Alumni Edition) Military Database (Alumni Edition) Science Database (Alumni Edition) Telecommunications (Alumni Edition) Computing Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Natural Science Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni Edition) Research Library (Alumni Edition) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central Advanced Technologies & Aerospace Database (1962 - current) ProQuest Agriculture & Environmental Science Database ProQuest Central Essentials Biological Science Collection AUTh Library subscriptions: ProQuest Central Business Premium Collection Technology Collection Natural Science Collection ProQuest One Community College ProQuest Materials Science Collection ProQuest Central Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student Research Library Prep SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database ProQuest Materials Science Database ABI/INFORM Professional Advanced ProQuest Engineering Collection Biological Sciences ABI/INFORM Collection Agriculture Science Database Computing Database Military Database ProQuest_Research Library ProQuest Science Journals Telecommunications Database Biological Science Database ProQuest Engineering Database Research Library (Corporate) ProQuest Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Environmental Science Database Materials Science Collection One Business (ProQuest) ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection Environmental Science Collection ProQuest Central Basic |
DatabaseTitle | CrossRef Agricultural Science Database ProQuest Business Collection (Alumni Edition) Research Library Prep Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest Military Collection ProQuest Central China ABI/INFORM Complete ProQuest Telecommunications Natural Science Collection Biological Science Collection Engineering Collection Career and Technical Education (Alumni Edition) Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Biological Science Collection ProQuest One Academic Eastern Edition Agricultural Science Collection ProQuest Technology Collection ProQuest Telecommunications (Alumni Edition) Biological Science Database ProQuest Business Collection Environmental Science Collection ProQuest Career and Technical Education ProQuest One Academic UKI Edition Environmental Science Database ProQuest One Academic ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Materials Science Collection ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Natural Science Collection ProQuest Biology Journals (Alumni Edition) ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ProQuest Central Korea Agricultural & Environmental Science Collection Materials Science Database ProQuest Research Library ABI/INFORM Complete (Alumni Edition) ProQuest Materials Science Collection ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest Military Collection (Alumni Edition) ProQuest SciTech Collection Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
DatabaseTitleList | Agricultural Science Database |
Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Applied Sciences Mathematics |
EISSN | 1095-7154 |
EndPage | 1885 |
ExternalDocumentID | 2597219441 10_1137_050627514 19203566 |
GroupedDBID | --Z -~X 08R 123 186 3V. 4.4 6TJ 7RQ 7WY 7X2 7XC 85S 88A 88I 8CJ 8FE 8FG 8FH 8FL 8G5 AAJWA AALVN AASXH ABDBF ABEHJ ABJCF ABKAD ABMZU ABPTK ABTAH ABUWG ACBEA ACGFO ACGOD ACIWK ACNCT ACPRK ADAJV ADBBV AENEX AFFNX AFKRA AFRAH ALMA_UNASSIGNED_HOLDINGS ANXRF ARAPS ATCPS AZQEC BBNVY BENPR BEZIV BGLVJ BHPHI BPHCQ CCPQU CS3 CZ9 D1I D1J D1K DQ2 DU5 DWQXO EAP EBS EJD EMK EST ESX FRNLG G8K GNUQQ GROUPED_ABI_INFORM_COMPLETE GUQSH H13 HCIFZ H~9 I-F IQODW K6- K60 K6V K6~ K7- KB. KC. L6V LK5 LK8 M0C M0K M0L M0N M1Q M2O M2P M7P M7R M7S MVM NHB P1Q P2P P62 PATMY PDBOC PQBIZ PQQKQ PROAC PTHSS PYCSY RJG RNS RSI TN5 TUS UQL VOH XFK XOL YNT YYP ZY4 AAYXX CITATION PQBZA 7XB 88K 8AL 8FK JQ2 L.- M2T MBDVC PQEST PQUKI PRINS Q9U U9A |
ID | FETCH-LOGICAL-c321t-987427e5728b924efca2c522347abdca752cba223ebfa348b8b008d923aed55d3 |
IEDL.DBID | BENPR |
ISSN | 0036-1410 |
IngestDate | Thu Oct 10 22:09:43 EDT 2024 Fri Aug 23 00:18:29 EDT 2024 Sun Oct 29 17:08:32 EDT 2023 |
IsDoiOpenAccess | false |
IsOpenAccess | true |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 6 |
Keywords | Perturbation theory Solution uniqueness Growth rate 35K57,35J65 Bifurcation theory Degree theory Steady state 35K55 chemostat Sufficient condition 92A17 Perturbation techniques coexistence solution Numerical stability stability Maximal solution |
Language | English |
License | CC BY 4.0 |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-c321t-987427e5728b924efca2c522347abdca752cba223ebfa348b8b008d923aed55d3 |
OpenAccessLink | http://ms.mcmaster.ca/wolkowic/Papers/SJM001860.pdf |
PQID | 923925310 |
PQPubID | 666308 |
PageCount | 26 |
ParticipantIDs | proquest_journals_923925310 crossref_primary_10_1137_050627514 pascalfrancis_primary_19203566 |
PublicationCentury | 2000 |
PublicationDate | 2007 2007-01-00 20070101 |
PublicationDateYYYYMMDD | 2007-01-01 |
PublicationDate_xml | – year: 2007 text: 2007 |
PublicationDecade | 2000 |
PublicationPlace | Philadelphia, PA |
PublicationPlace_xml | – name: Philadelphia, PA – name: Philadelphia |
PublicationTitle | SIAM journal on mathematical analysis |
PublicationYear | 2007 |
Publisher | Society for Industrial and Applied Mathematics |
Publisher_xml | – name: Society for Industrial and Applied Mathematics |
References | Ruan W. (R26) 1995; 8 R21 R20 R23 R22 R25 R24 R28 R1 R2 R3 R4 R6 R7 R8 R9 R10 R32 R12 R34 R33 R14 R36 R13 R16 R15 R18 R17 |
References_xml | – ident: R15 doi: 10.1016/S0009-2509(96)00385-5 – ident: R21 doi: 10.1016/S0022-5193(86)80226-0 – ident: R9 doi: 10.1080/03605309208820844 – ident: R25 doi: 10.1002/bit.260260819 – ident: R28 doi: 10.1016/0009-2509(88)87125-2 – ident: R8 doi: 10.1090/S0002-9947-97-01842-4 – ident: R14 doi: 10.1137/0153051 – ident: R10 doi: 10.1126/science.7268409 – ident: R23 doi: 10.1007/BF00163028 – volume: 8 start-page: 371 issn: 0893-4983 year: 1995 ident: R26 publication-title: Differential Integral Equations contributor: fullname: Ruan W. – ident: R7 doi: 10.1017/S0308210500023064 – ident: R20 doi: 10.1098/rstb.1988.0059 – ident: R1 doi: 10.1073/pnas.78.10.6324 – ident: R13 doi: 10.1137/0152029 – ident: R2 doi: 10.1016/0022-1236(71)90015-2 – ident: R3 doi: 10.1007/BF00282325 – ident: R18 doi: 10.1007/BF00180136 – ident: R36 doi: 10.1016/S0096-3003(02)00732-4 – ident: R12 doi: 10.1007/BF00178774 – ident: R16 doi: 10.1016/j.mbs.2003.07.004 – ident: R24 doi: 10.1142/S0218127406015246 – ident: R33 doi: 10.1016/S0362-546X(98)00163-1 – ident: R17 doi: 10.1007/BF00163024 – ident: R22 doi: 10.1016/S0025-5564(97)10010-4 – ident: R32 doi: 10.1137/S0036139903423285 – ident: R34 doi: 10.1006/jdeq.2000.3870 – ident: R4 doi: 10.1016/0022-247X(83)90098-7 – ident: R6 doi: 10.1006/jdeq.1996.0132 |
SSID | ssj0016490 |
Score | 2.0494196 |
Snippet | This paper deals with a chemostat model with an inhibitor in the context of competition between plasmid-bearing and plasmid-free organisms. First, sufficient... |
SourceID | proquest crossref pascalfrancis |
SourceType | Aggregation Database Index Database |
StartPage | 1860 |
SubjectTerms | Applied mathematics Competition Exact sciences and technology Global analysis, analysis on manifolds Mathematical analysis Mathematics Operator theory Organisms Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
Title | The effect of inhibitor on the plasmid-bearing and plasmid-free model in the unstirred chemostat |
URI | https://www.proquest.com/docview/923925310 |
Volume | 38 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3fS9xAEB4878VSaj0rvWqPpfi6eEk2m81T8fRSLSgiHtxb3F_BA02uyfX_72yyFxGhj0kGArMzO9_OzH4DcBopF_bThEoMZpSlglPBNadSYHyTiSpYO4fs5pZfLdjvZbz0vTmNb6vc7ontRm0q7XLkZwhE0hANZvpz_Ye6oVGuuOonaAxgGAbMVWmHs_nt3X1fRuAsnW5Zd11Do6cWChypT9wS9AbsTUD6uJYN6qbohlq825_boJN9hk8eLZLzbnkPYMeWI9j3yJF4v2xG8OGmZ19tDuER1550tMSkKsh1-bRS6Lg1qUqCYuQOEfPLytAZWjlGLiJL07_LamuJG5D2TFad9MK1E9Q1_s-RC1TuBtIXWGTzh4sr6icpUB2FwYamAk_AiY2TUCg8cNlCy1Aj8opYIpXRMolDrSQ-W1XIiAkl0BuFQZ1La-LYREewW1al_Qok4qrg2l2vTQQKslQXgZE8CBTXRqV2DD-26szXHWFG3h40oiTvdT6GyRtFv0qm4TRChDmG463mc-9UTd6bwLf_fj2GvS4B6_IkJ7C7qf_a74gcNmoCA5H9msDwfHY5yybeWv4BHK3DtA |
link.rule.ids | 315,786,790,4043,12792,21416,27954,27955,27956,33406,33777,43633,43838 |
linkProvider | ProQuest |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LT9wwEB612wMgRIFSdaEFC3G1uokdxzkhqLpdHos4sBK34FfESjRZku3_Z5x4gxBSj0lGijSexzf2-BuAE6Z92s9SqjCZUZ5JQaUwgiqJ-U2luuDtHLLpjZjM-OV9ch96c5rQVrmKiW2gtpXxe-Q_EYhkMRrM6HTxTP3QKH-4GiZofIRPnAnmzVyO__SHCIJnoxXnrm9nDMRCkaf0SVp63oi_SUebC9WgZopupMW76NymnPE2bAWsSM66xd2BD67chc8BN5Lglc0ubEx77tXmCzzgypOOlJhUBbkoH-ca3bYmVUlQjNwiXv47t_QcbRzzFlGl7d-Na-eIH4_2ROad9Mw3E9Q1_s9TC1T-_tEezMa_735NaJijQA2LoyXNJNa_qUvSWGost1xhVGwQdzGeKm2NSpPYaIXPTheKcakl-qK0qHHlbJJY9hUGZVW6b0CY0IUw_nJtKlGQZ6aIrBJRpIWxOnNDOF6pM190dBl5W2awNO91PoTDN4p-lcziEUN8OYSDlebz4FJN3hvA_n-_HsHa5G56nV9f3FwdwHq3Fet3TL7DYFn_cz8QQyz1YWspL2L9wuM |
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=The+effect+of+inhibitor+on+the+plasmid-bearing+and+plasmid-free+model+in+the+unstirred+chemostat&rft.jtitle=SIAM+journal+on+mathematical+analysis&rft.au=JIANHUA+WU&rft.au=HUA+NIE&rft.au=WOLKOWICZ%2C+Gail+S.+K&rft.date=2007&rft.pub=Society+for+Industrial+and+Applied+Mathematics&rft.issn=0036-1410&rft.eissn=1095-7154&rft.volume=38&rft.issue=6&rft.spage=1860&rft.epage=1885&rft_id=info:doi/10.1137%2F050627514&rft.externalDBID=n%2Fa&rft.externalDocID=19203566 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0036-1410&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0036-1410&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0036-1410&client=summon |