Periodic solution and control optimization of a prey-predator model with two types of harvesting
In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differentia...
Saved in:
| Published in | Advances in difference equations Vol. 2018; no. 1; pp. 1 - 14 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
25.01.2018
SpringerOpen |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained. |
|---|---|
| AbstractList | In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained. Abstract In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained. |
| ArticleNumber | 41 |
| Author | Liu, Hongxia Wang, Jianmei Cheng, Huidong Wang, Yanhui |
| Author_xml | – sequence: 1 givenname: Jianmei surname: Wang fullname: Wang, Jianmei organization: College of Mathematics and Systems Science, Shandong University of Science and Technology – sequence: 2 givenname: Huidong surname: Cheng fullname: Cheng, Huidong email: chd900517@sdust.edu.cn organization: College of Mathematics and Systems Science, Shandong University of Science and Technology – sequence: 3 givenname: Hongxia surname: Liu fullname: Liu, Hongxia organization: College of Mathematics and Systems Science, Shandong University of Science and Technology, State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology – sequence: 4 givenname: Yanhui surname: Wang fullname: Wang, Yanhui organization: College of Mathematics and Systems Science, Shandong University of Science and Technology, State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology |
| BookMark | eNp9kMFuGyEQhlGUSEmcPEBuvMC2gGGBYxSlraVI6aE90wFmHaz1YgFu5D5913ZV9dTLzGhm_k_6_1tyOeUJCXng7APnpv9Y-bLvRce46bi0trMX5Ib3RnfcSH35z3xNbmvdMCasNOaG_PiKJeWYAq153LeUJwpTpCFPreSR5l1L2_QLToc8UKC7goduLhFaLnSbI470PbU32t4zbYcd1uPfG5SfWFua1nfkaoCx4v2fviDfPz1_e_rSvbx-Xj09vnRhaXXrNIICZIJ7hpYJYaSZbZlB9hI9BBhA6IFFr0BJ7oWS1puIdolKQ6-8Xi7I6syNGTZuV9IWysFlSO60yGXtoLQURnSx1wwFqhhEkDAwE5T3WiqUXqPqYWbxMyuUXGvB4S-PM3eM253jdnPc7hi3s7NGnDV1_p3WWNwm78s0W_6P6DfZMYby |
| CitedBy_id | crossref_primary_10_1515_zna_2021_0131 crossref_primary_10_1016_j_amc_2019_06_026 crossref_primary_10_3390_math7070591 crossref_primary_10_1007_s12652_020_01806_5 crossref_primary_10_1016_j_cam_2020_112920 crossref_primary_10_3390_math7121172 crossref_primary_10_1080_00207160_2020_1802018 crossref_primary_10_1186_s13662_018_1820_7 crossref_primary_10_1142_S0218127418500992 crossref_primary_10_3934_dcdss_2020259 crossref_primary_10_1007_s40815_018_0532_1 crossref_primary_10_1142_S179352451850064X crossref_primary_10_1007_s40815_019_00769_w crossref_primary_10_1155_2019_3859815 crossref_primary_10_1142_S0218127419501529 crossref_primary_10_1186_s13662_019_2211_4 crossref_primary_10_1186_s13662_018_1933_z crossref_primary_10_1155_2019_4873290 crossref_primary_10_1142_S0218127420502430 crossref_primary_10_1155_2018_4945728 crossref_primary_10_1109_ACCESS_2019_2922748 crossref_primary_10_1109_ACCESS_2019_2938772 crossref_primary_10_1016_j_chaos_2019_01_029 crossref_primary_10_1155_2019_4976351 crossref_primary_10_1155_2019_5308014 crossref_primary_10_1155_2018_9801240 crossref_primary_10_1186_s13662_019_2002_y crossref_primary_10_1155_2020_8974763 crossref_primary_10_1186_s13662_018_1615_x crossref_primary_10_1155_2019_7254121 crossref_primary_10_1186_s13662_018_1735_3 crossref_primary_10_1155_2020_5726895 crossref_primary_10_1155_2020_2376374 crossref_primary_10_1007_s12555_018_0297_1 crossref_primary_10_3390_math11143254 |
| Cites_doi | 10.1007/s11071-014-1486-y 10.1186/s13662-017-1077-6 10.1142/S0218339007002222 10.1016/j.cnsns.2015.07.013 10.1016/j.nonrwa.2015.05.012 10.1007/BF00280586 10.1007/s11071-013-0834-7 10.1007/s11071-015-2586-z 10.1007/s11071-013-1194-z 10.1016/j.matcom.2009.01.003 10.1016/j.jfranklin.2016.06.035 10.1186/s13662-017-1163-9 10.1016/j.nahs.2017.04.003 10.1016/j.cnsns.2017.09.005 10.1186/s13662-017-1300-5 10.1016/j.cam.2015.01.017 10.1007/s11071-013-0839-2 10.1155/2017/3742197 10.1016/j.jmaa.2005.11.048 10.1186/s13660-017-1418-8 10.1016/j.mbs.2016.06.006 10.1080/00207721.2017.1384861 10.1142/S0218127417501085 10.1186/s13662-017-1426-5 10.1007/s002850100095 10.1016/j.chaos.2017.04.037 10.1186/s13662-017-1363-3 10.1155/2017/4820183 10.1007/s11071-010-9840-1 10.1186/s13662-017-1289-9 10.1016/j.nahs.2016.09.002 10.1002/mma.3467 10.1016/j.biosystems.2009.06.001 10.1142/S1793524510000957 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2018 |
| Copyright_xml | – notice: The Author(s) 2018 |
| DBID | C6C AAYXX CITATION DOA |
| DOI | 10.1186/s13662-018-1499-9 |
| DatabaseName | Springer Open Access CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: C6C name: Springer Open Access url: http://www.springeropen.com/ sourceTypes: Publisher – sequence: 2 dbid: DOA name: Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1687-1847 |
| EndPage | 14 |
| ExternalDocumentID | oai_doaj_org_article_d670e2e5dc2c4af08c5bb745e4b7e56a 10_1186_s13662_018_1499_9 |
| GrantInformation_xml | – fundername: Shandong Provincial Natural Science Foundation, China grantid: S2015SF002 – fundername: SDUST Research Fund grantid: 2014TDJH102 – fundername: National Natural Science Foundation of China grantid: 11371230; 11501331 funderid: http://dx.doi.org/10.13039/501100001809 |
| GroupedDBID | -A0 0R~ 23M 2WC 3V. 4.4 40G 5GY 5VS 6J9 8FE 8FG 8R4 8R5 AAFWJ AAKKN AAPBV AAYZJ ABDBF ABJCF ABPTK ABUWG ACACY ACGFO ACGFS ACIPV ACIWK ADBBV ADINQ AEGXH AENEX AFGXO AFKRA AFPKN AHBXF AHBYD AHYZX AIAGR ALMA_UNASSIGNED_HOLDINGS AMKLP AMTXH ARAPS AZQEC BAPOH BCNDV BENPR BGLVJ BPHCQ C24 C6C CCPQU CS3 DWQXO EBS EJD ESX GNUQQ GROUPED_DOAJ HCIFZ J9A K6V K7- KQ8 L6V M0N M7S M~E OK1 P2P P62 PIMPY PQQKQ PROAC PTHSS Q2X REM RHU RNS RSV SMT SOJ TUS U2A UPT ~8M AAYXX CITATION H13 |
| ID | FETCH-LOGICAL-c397t-7ea5ae021b0e90228481868f464ebacafa27f0db5a541b2549b8de93e57a65b73 |
| IEDL.DBID | 40G |
| ISSN | 1687-1847 |
| IngestDate | Tue Oct 22 15:01:33 EDT 2024 Fri Aug 23 01:24:05 EDT 2024 Sat Dec 16 12:12:28 EST 2023 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | 34C25 prey-predator model 34A37 92B05 optimization 34D20 state-dependent impulse order-1 periodic solution stability |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c397t-7ea5ae021b0e90228481868f464ebacafa27f0db5a541b2549b8de93e57a65b73 |
| OpenAccessLink | http://link.springer.com/10.1186/s13662-018-1499-9 |
| PageCount | 14 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_d670e2e5dc2c4af08c5bb745e4b7e56a crossref_primary_10_1186_s13662_018_1499_9 springer_journals_10_1186_s13662_018_1499_9 |
| PublicationCentury | 2000 |
| PublicationDate | 2018-01-25 |
| PublicationDateYYYYMMDD | 2018-01-25 |
| PublicationDate_xml | – month: 01 year: 2018 text: 2018-01-25 day: 25 |
| PublicationDecade | 2010 |
| PublicationPlace | Cham |
| PublicationPlace_xml | – name: Cham |
| PublicationTitle | Advances in difference equations |
| PublicationTitleAbbrev | Adv Differ Equ |
| PublicationYear | 2018 |
| Publisher | Springer International Publishing SpringerOpen |
| Publisher_xml | – name: Springer International Publishing – name: SpringerOpen |
| References | Wang, Cheng, Meng, Pradeep (CR45) 2017; 2017 Zhang, Meng, Song (CR12) 2011; 64 Zhao, Li, Meng (CR36) 2015; 2015 Xiao, Li, Han (CR7) 2006; 324 Zhang, Meng, Feng, Zhang (CR14) 2017; 26 Lv, Wang, Meng (CR39) 2017; 2017 Huang, Liu, Song, Chen (CR40) 2013; 73 Meng, Wang, Zhang (CR11) 2016; 6 Nie, Teng, Hu, Peng (CR25) 2009; 98 Zhang, Meng, Liu, Zhang (CR33) 2014; 78 Huang, Cao, Xiao, Alsaedi, Hayat (CR21) 2017; 292 Leng, Feng, Meng (CR37) 2017; 2017 Cheng, Zhang, Wang (CR29) 2012; 2012 Zhang, Zhang, Meng, Zhang (CR48) 2016; 84 Bian, Zhao, Song, Yue (CR4) 2017; 2017 Chen (CR43) 2011; 12 Zhang, Ma, Meng (CR9) 2017; 2017 Jiao, Cai, Li (CR18) 2016; 353 Cheng, Wang, Zhang (CR47) 2012; 2012 Chen, Chen (CR8) 2010; 3 Huang, Song (CR26) 2014; 2014 Zhang, Georgescu, Zhang (CR30) 2016; 31 Meng, Zhang (CR15) 2016; 39 Zhang, Ma, Meng, Zhang (CR23) 2015; 266 Cheng, Wang, Zhang (CR31) 2012; 2012 Lv, Wang (CR38) 2017; 2017 Brauer, Soudack (CR5) 1979; 8 Wang, Jiang, Wang (CR10) 2013; 73 Zhang, Ma, Meng (CR16) 2017; 48 Huang, Cao, Xiao, Alsaedi, Alsaadi (CR22) 2017; 293 Sun, Zhang, Tian (CR42) 2016; 279 Liu, Tian, Kang (CR44) 2012; 5 Liu, Wang, Meng, Gao (CR2) 2017; 2017 Pei, Li, Chen (CR17) 2009; 79 Pal, Mahapatra (CR1) 2014; 242 Huang, Cao, Xiao, Alsaedi, Hayat (CR20) 2018; 57 Tian, Zhang, Sun (CR32) 2017; 23 Jiang, Wang (CR13) 2017; 27 Liu, Meng (CR3) 2017; 2017 Huang, Meng, Cao, Alsaedi, Alsaadi (CR19) 2017; 100 Wei, Chen (CR27) 2014; 76 Miao, Zhang, Zhang, Pradeep (CR34) 2017; 2017 Jiao, Chen, Long (CR24) 2008; 15 Xiao, Dai, Xu, Bao (CR41) 2015; 26 Zhao, Liu, Zhang, Meng (CR46) 2014; 2014 Martin, Ruan (CR6) 2001; 43 Miao, Wang, Zhang, Wang, Pradeep (CR35) 2017; 2017 Yang, Tang (CR28) 2016; 291 T Zhang (1499_CR16) 2017; 48 A Martin (1499_CR6) 2001; 43 C Huang (1499_CR19) 2017; 100 C Wei (1499_CR27) 2014; 76 X Leng (1499_CR37) 2017; 2017 H Cheng (1499_CR47) 2012; 2012 H Cheng (1499_CR29) 2012; 2012 T Zhang (1499_CR23) 2015; 266 J Wang (1499_CR45) 2017; 2017 F Bian (1499_CR4) 2017; 2017 L Chen (1499_CR43) 2011; 12 H Zhang (1499_CR30) 2016; 31 A Miao (1499_CR35) 2017; 2017 B Liu (1499_CR44) 2012; 5 X Lv (1499_CR39) 2017; 2017 H Cheng (1499_CR31) 2012; 2012 J Yang (1499_CR28) 2016; 291 T Zhang (1499_CR12) 2011; 64 S Zhang (1499_CR14) 2017; 26 Q Xiao (1499_CR41) 2015; 26 L Liu (1499_CR3) 2017; 2017 C Huang (1499_CR22) 2017; 293 X Meng (1499_CR15) 2016; 39 L Chen (1499_CR8) 2010; 3 Y Pei (1499_CR17) 2009; 79 K Sun (1499_CR42) 2016; 279 W Zhao (1499_CR36) 2015; 2015 D Xiao (1499_CR7) 2006; 324 Y Wang (1499_CR10) 2013; 73 X Meng (1499_CR11) 2016; 6 C Huang (1499_CR20) 2018; 57 W Lv (1499_CR38) 2017; 2017 C Huang (1499_CR21) 2017; 292 A Miao (1499_CR34) 2017; 2017 Z Jiang (1499_CR13) 2017; 27 J Jiao (1499_CR18) 2016; 353 F Brauer (1499_CR5) 1979; 8 T Zhang (1499_CR33) 2014; 78 Y Tian (1499_CR32) 2017; 23 J Jiao (1499_CR24) 2008; 15 D Pal (1499_CR1) 2014; 242 L Nie (1499_CR25) 2009; 98 M Huang (1499_CR26) 2014; 2014 G Liu (1499_CR2) 2017; 2017 T Zhang (1499_CR9) 2017; 2017 W Zhao (1499_CR46) 2014; 2014 M Huang (1499_CR40) 2013; 73 T Zhang (1499_CR48) 2016; 84 |
| References_xml | – volume: 78 start-page: 921 issue: 2 year: 2014 end-page: 938 ident: CR33 article-title: Periodic solution of a pest management Gompertz model with impulsive state feedback control publication-title: Nonlinear Dyn. doi: 10.1007/s11071-014-1486-y contributor: fullname: Zhang – volume: 2017 issue: 1 year: 2017 ident: CR3 article-title: Optimal harvesting control and dynamics of two-species stochastic model with delays publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1077-6 contributor: fullname: Meng – volume: 15 start-page: 409 issue: 03 year: 2008 end-page: 416 ident: CR24 article-title: Pulse fishing policy for a stage-structured model with state-dependent harvesting publication-title: J. Biol. Syst. doi: 10.1142/S0218339007002222 contributor: fullname: Long – volume: 31 start-page: 83 issue: 1 year: 2016 end-page: 107 ident: CR30 article-title: Periodic patterns and Pareto efficiency of state dependent impulsive controls regulating interactions between wild and transgenic mosquito populations publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2015.07.013 contributor: fullname: Zhang – volume: 26 start-page: 263 year: 2015 end-page: 273 ident: CR41 article-title: Homoclinic bifurcation for a general state-dependent Kolmogorov type predator-prey model with harvesting publication-title: Nonlinear Anal., Real World Appl. doi: 10.1016/j.nonrwa.2015.05.012 contributor: fullname: Bao – volume: 8 start-page: 55 issue: 1 year: 1979 end-page: 71 ident: CR5 article-title: Stability regions in predator-prey systems with constant-rate prey harvesting publication-title: J. Math. Biol. doi: 10.1007/BF00280586 contributor: fullname: Soudack – volume: 292 start-page: 210 year: 2017 end-page: 227 ident: CR21 article-title: Bifurcations in a delayed fractional complex-valued neural network publication-title: Appl. Math. Comput. contributor: fullname: Hayat – volume: 73 start-page: 815 year: 2013 end-page: 826 ident: CR40 article-title: Periodic solutions and homoclinic bifurcation of a predator-prey system with two types of harvesting publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-0834-7 contributor: fullname: Chen – volume: 84 start-page: 1529 issue: 3 year: 2016 end-page: 1539 ident: CR48 article-title: Geometric analysis of a pest management model with Holling’s type III functional response and nonlinear state feedback control publication-title: Nonlinear Dyn. doi: 10.1007/s11071-015-2586-z contributor: fullname: Zhang – volume: 76 start-page: 1109 issue: 2 year: 2014 end-page: 1117 ident: CR27 article-title: Periodic solution and heteroclinic bifurcation in a predator-prey system with Allee effect and impulsive harvesting publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-1194-z contributor: fullname: Chen – volume: 2017 issue: 3 year: 2017 ident: CR2 article-title: Extinction and persistence in mean of a novel delay impulsive stochastic infected predator-prey system with jumps publication-title: Complexity contributor: fullname: Gao – volume: 79 start-page: 2994 issue: 10 year: 2009 end-page: 3008 ident: CR17 article-title: Continuous and impulsive harvesting strategies in a stage-structured predator-prey model with time delay publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2009.01.003 contributor: fullname: Chen – volume: 12 start-page: 1 issue: 1 year: 2011 end-page: 9 ident: CR43 article-title: Pest control and geometric theory of semi-continuous dynamical system publication-title: J. Beihua Univ. Nat. Sci. contributor: fullname: Chen – volume: 353 start-page: 3818 issue: 15 year: 2016 end-page: 3834 ident: CR18 article-title: Dynamics of a periodic switched predator-prey system with impulsive harvesting and hibernation of prey population publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2016.06.035 contributor: fullname: Li – volume: 2017 issue: 1 year: 2017 ident: CR9 article-title: Global dynamics of a delayed chemostat model with harvest by impulsive flocculant input publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1163-9 contributor: fullname: Meng – volume: 266 start-page: 95 year: 2015 end-page: 107 ident: CR23 article-title: Periodic solution of a prey-predator model with nonlinear state feedback control publication-title: Appl. Math. Comput. contributor: fullname: Zhang – volume: 242 start-page: 748 year: 2014 end-page: 763 ident: CR1 article-title: A bioeconomic modeling of two-prey and one-predator fishery model with optimal harvesting policy through hybridization approach publication-title: Appl. Math. Comput. contributor: fullname: Mahapatra – volume: 26 start-page: 19 year: 2017 end-page: 37 ident: CR14 article-title: Dynamics analysis and numerical simulations of a stochastic non-autonomous predator-prey system with impulsive effects publication-title: Nonlinear Anal. Hybrid Syst. doi: 10.1016/j.nahs.2017.04.003 contributor: fullname: Zhang – volume: 57 start-page: 1 year: 2018 end-page: 13 ident: CR20 article-title: Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2017.09.005 contributor: fullname: Hayat – volume: 2017 issue: 1 year: 2017 ident: CR45 article-title: Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1300-5 contributor: fullname: Pradeep – volume: 291 start-page: 225 year: 2016 end-page: 241 ident: CR28 article-title: Holling type II predator-prey model with nonlinear pulse as state-dependent feedback control publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2015.01.017 contributor: fullname: Tang – volume: 2012 start-page: 30 issue: 12 year: 2012 end-page: 44 ident: CR47 article-title: Multi-state dependent impulsive control for Holling I predator-prey model publication-title: Discrete Dyn. Nat. Soc. contributor: fullname: Zhang – volume: 73 start-page: 881 issue: 1 year: 2013 end-page: 896 ident: CR10 article-title: Stability and global Hopf bifurcation in toxic phytoplankton-zooplankton model with delay and selective harvesting publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-0839-2 contributor: fullname: Wang – volume: 2017 year: 2017 ident: CR4 article-title: Dynamical analysis of a class of prey-predator model with Beddington-Deangelis functional response, stochastic perturbation, and impulsive toxicant input publication-title: Complexity doi: 10.1155/2017/3742197 contributor: fullname: Yue – volume: 2012 year: 2012 ident: CR31 article-title: Multi-state dependent impulsive control for pest management publication-title: J. Appl. Math. contributor: fullname: Zhang – volume: 2014 year: 2014 ident: CR26 article-title: Periodic solutions and homoclinic bifurcations of two predator-prey systems with nonmonotonic functional response and impulsive harvesting publication-title: J. Appl. Math. contributor: fullname: Song – volume: 324 start-page: 14 issue: 1 year: 2006 end-page: 29 ident: CR7 article-title: Dynamics in a ratio-dependent predator-prey model with predator harvesting publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.11.048 contributor: fullname: Han – volume: 2017 year: 2017 ident: CR37 article-title: Stochastic inequalities and applications to dynamics analysis of a novel SIVS epidemic model with jumps publication-title: J. Inequal. Appl. doi: 10.1186/s13660-017-1418-8 contributor: fullname: Meng – volume: 279 start-page: 13 year: 2016 end-page: 26 ident: CR42 article-title: Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate publication-title: Math. Biosci. doi: 10.1016/j.mbs.2016.06.006 contributor: fullname: Tian – volume: 48 start-page: 3459 issue: 16 year: 2017 end-page: 3469 ident: CR16 article-title: Impulsive control of a continuous-culture and flocculation harvest chemostat model publication-title: Int. J. Syst. Sci. doi: 10.1080/00207721.2017.1384861 contributor: fullname: Meng – volume: 5 start-page: 675 issue: 03 year: 2012 ident: CR44 article-title: Dynamics on a Holling II predator-prey model with state-dependent impulsive control publication-title: Int. J. Biomath. contributor: fullname: Kang – volume: 27 issue: 07 year: 2017 ident: CR13 article-title: Global Hopf bifurcation for a predator-prey system with three delays publication-title: Int. J. Bifurc. Chaos doi: 10.1142/S0218127417501085 contributor: fullname: Wang – volume: 2017 issue: 1 year: 2017 ident: CR38 article-title: Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1426-5 contributor: fullname: Wang – volume: 2012 year: 2012 ident: CR29 article-title: Existence and attractiveness of order one periodic solution of a Holling I predator-prey model publication-title: Abstr. Appl. Anal. contributor: fullname: Wang – volume: 43 start-page: 247 issue: 3 year: 2001 end-page: 267 ident: CR6 article-title: Predator-prey models with delay and prey harvesting publication-title: J. Math. Biol. doi: 10.1007/s002850100095 contributor: fullname: Ruan – volume: 6 start-page: 865 issue: 3 year: 2016 end-page: 875 ident: CR11 article-title: Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment publication-title: J. Appl. Anal. Comput. contributor: fullname: Zhang – volume: 100 start-page: 31 year: 2017 end-page: 44 ident: CR19 article-title: New bifurcation results for fractional BAM neural network with leakage delay publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2017.04.037 contributor: fullname: Alsaadi – volume: 2015 year: 2015 ident: CR36 article-title: Dynamical analysis of SIR epidemic model with nonlinear pulse vaccination and lifelong immunity publication-title: Discrete Dyn. Nat. Soc. contributor: fullname: Meng – volume: 293 start-page: 293 year: 2017 end-page: 310 ident: CR22 article-title: Controlling bifurcation in a delayed fractional predator-prey system with incommensurate orders publication-title: Appl. Math. Comput. contributor: fullname: Alsaadi – volume: 2017 issue: 1 year: 2017 ident: CR39 article-title: Global analysis of a new nonlinear stochastic differential competition system with impulsive effect publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1363-3 contributor: fullname: Meng – volume: 2017 year: 2017 ident: CR34 article-title: Threshold dynamics of a stochastic SIR model with vertical transmission and vaccination publication-title: Comput. Math. Methods Med. doi: 10.1155/2017/4820183 contributor: fullname: Pradeep – volume: 64 start-page: 1 issue: 1 year: 2011 end-page: 12 ident: CR12 article-title: The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments publication-title: Nonlinear Dyn. doi: 10.1007/s11071-010-9840-1 contributor: fullname: Song – volume: 2017 year: 2017 ident: CR35 article-title: Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1289-9 contributor: fullname: Pradeep – volume: 23 start-page: 122 year: 2017 end-page: 141 ident: CR32 article-title: Dynamics analysis of a pest management prey-predator model by means of interval state monitoring and control publication-title: Nonlinear Anal. Hybrid Syst. doi: 10.1016/j.nahs.2016.09.002 contributor: fullname: Sun – volume: 39 start-page: 177 issue: 2 year: 2016 end-page: 188 ident: CR15 article-title: Evolutionary dynamics in a Lotka-Volterra competition model with impulsive periodic disturbance publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3467 contributor: fullname: Zhang – volume: 98 start-page: 67 issue: 2 year: 2009 end-page: 72 ident: CR25 article-title: The dynamics of a Lotka-Volterra predator-prey model with state dependent impulsive harvest for predator publication-title: Biosystems doi: 10.1016/j.biosystems.2009.06.001 contributor: fullname: Peng – volume: 3 start-page: 205 issue: 02 year: 2010 end-page: 223 ident: CR8 article-title: Global analysis of a harvested predator-prey model incorporating a constant prey refuge publication-title: Int. J. Biomath. doi: 10.1142/S1793524510000957 contributor: fullname: Chen – volume: 2014 issue: 1 year: 2014 ident: CR46 article-title: Geometric analysis of an integrated pest management model including two state impulses publication-title: Abstr. Appl. Anal. contributor: fullname: Meng – volume: 324 start-page: 14 issue: 1 year: 2006 ident: 1499_CR7 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2005.11.048 contributor: fullname: D Xiao – volume: 291 start-page: 225 year: 2016 ident: 1499_CR28 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2015.01.017 contributor: fullname: J Yang – volume: 266 start-page: 95 year: 2015 ident: 1499_CR23 publication-title: Appl. Math. Comput. contributor: fullname: T Zhang – volume: 57 start-page: 1 year: 2018 ident: 1499_CR20 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2017.09.005 contributor: fullname: C Huang – volume: 43 start-page: 247 issue: 3 year: 2001 ident: 1499_CR6 publication-title: J. Math. Biol. doi: 10.1007/s002850100095 contributor: fullname: A Martin – volume: 98 start-page: 67 issue: 2 year: 2009 ident: 1499_CR25 publication-title: Biosystems doi: 10.1016/j.biosystems.2009.06.001 contributor: fullname: L Nie – volume: 2017 year: 2017 ident: 1499_CR4 publication-title: Complexity doi: 10.1155/2017/3742197 contributor: fullname: F Bian – volume: 293 start-page: 293 year: 2017 ident: 1499_CR22 publication-title: Appl. Math. Comput. contributor: fullname: C Huang – volume: 2017 year: 2017 ident: 1499_CR37 publication-title: J. Inequal. Appl. doi: 10.1186/s13660-017-1418-8 contributor: fullname: X Leng – volume: 2014 issue: 1 year: 2014 ident: 1499_CR46 publication-title: Abstr. Appl. Anal. contributor: fullname: W Zhao – volume: 2012 start-page: 30 issue: 12 year: 2012 ident: 1499_CR47 publication-title: Discrete Dyn. Nat. Soc. contributor: fullname: H Cheng – volume: 26 start-page: 19 year: 2017 ident: 1499_CR14 publication-title: Nonlinear Anal. Hybrid Syst. doi: 10.1016/j.nahs.2017.04.003 contributor: fullname: S Zhang – volume: 2017 issue: 1 year: 2017 ident: 1499_CR39 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1363-3 contributor: fullname: X Lv – volume: 15 start-page: 409 issue: 03 year: 2008 ident: 1499_CR24 publication-title: J. Biol. Syst. doi: 10.1142/S0218339007002222 contributor: fullname: J Jiao – volume: 76 start-page: 1109 issue: 2 year: 2014 ident: 1499_CR27 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-1194-z contributor: fullname: C Wei – volume: 2017 issue: 1 year: 2017 ident: 1499_CR45 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1300-5 contributor: fullname: J Wang – volume: 73 start-page: 881 issue: 1 year: 2013 ident: 1499_CR10 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-0839-2 contributor: fullname: Y Wang – volume: 79 start-page: 2994 issue: 10 year: 2009 ident: 1499_CR17 publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2009.01.003 contributor: fullname: Y Pei – volume: 2017 issue: 3 year: 2017 ident: 1499_CR2 publication-title: Complexity contributor: fullname: G Liu – volume: 2017 issue: 1 year: 2017 ident: 1499_CR3 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1077-6 contributor: fullname: L Liu – volume: 100 start-page: 31 year: 2017 ident: 1499_CR19 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2017.04.037 contributor: fullname: C Huang – volume: 2017 year: 2017 ident: 1499_CR35 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1289-9 contributor: fullname: A Miao – volume: 242 start-page: 748 year: 2014 ident: 1499_CR1 publication-title: Appl. Math. Comput. contributor: fullname: D Pal – volume: 31 start-page: 83 issue: 1 year: 2016 ident: 1499_CR30 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2015.07.013 contributor: fullname: H Zhang – volume: 2017 issue: 1 year: 2017 ident: 1499_CR9 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1163-9 contributor: fullname: T Zhang – volume: 39 start-page: 177 issue: 2 year: 2016 ident: 1499_CR15 publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3467 contributor: fullname: X Meng – volume: 2014 year: 2014 ident: 1499_CR26 publication-title: J. Appl. Math. contributor: fullname: M Huang – volume: 2017 year: 2017 ident: 1499_CR34 publication-title: Comput. Math. Methods Med. doi: 10.1155/2017/4820183 contributor: fullname: A Miao – volume: 2015 year: 2015 ident: 1499_CR36 publication-title: Discrete Dyn. Nat. Soc. contributor: fullname: W Zhao – volume: 64 start-page: 1 issue: 1 year: 2011 ident: 1499_CR12 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-010-9840-1 contributor: fullname: T Zhang – volume: 6 start-page: 865 issue: 3 year: 2016 ident: 1499_CR11 publication-title: J. Appl. Anal. Comput. contributor: fullname: X Meng – volume: 2012 year: 2012 ident: 1499_CR29 publication-title: Abstr. Appl. Anal. contributor: fullname: H Cheng – volume: 353 start-page: 3818 issue: 15 year: 2016 ident: 1499_CR18 publication-title: J. Franklin Inst. doi: 10.1016/j.jfranklin.2016.06.035 contributor: fullname: J Jiao – volume: 23 start-page: 122 year: 2017 ident: 1499_CR32 publication-title: Nonlinear Anal. Hybrid Syst. doi: 10.1016/j.nahs.2016.09.002 contributor: fullname: Y Tian – volume: 12 start-page: 1 issue: 1 year: 2011 ident: 1499_CR43 publication-title: J. Beihua Univ. Nat. Sci. contributor: fullname: L Chen – volume: 5 start-page: 675 issue: 03 year: 2012 ident: 1499_CR44 publication-title: Int. J. Biomath. contributor: fullname: B Liu – volume: 3 start-page: 205 issue: 02 year: 2010 ident: 1499_CR8 publication-title: Int. J. Biomath. doi: 10.1142/S1793524510000957 contributor: fullname: L Chen – volume: 279 start-page: 13 year: 2016 ident: 1499_CR42 publication-title: Math. Biosci. doi: 10.1016/j.mbs.2016.06.006 contributor: fullname: K Sun – volume: 48 start-page: 3459 issue: 16 year: 2017 ident: 1499_CR16 publication-title: Int. J. Syst. Sci. doi: 10.1080/00207721.2017.1384861 contributor: fullname: T Zhang – volume: 73 start-page: 815 year: 2013 ident: 1499_CR40 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-013-0834-7 contributor: fullname: M Huang – volume: 26 start-page: 263 year: 2015 ident: 1499_CR41 publication-title: Nonlinear Anal., Real World Appl. doi: 10.1016/j.nonrwa.2015.05.012 contributor: fullname: Q Xiao – volume: 84 start-page: 1529 issue: 3 year: 2016 ident: 1499_CR48 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-015-2586-z contributor: fullname: T Zhang – volume: 2012 year: 2012 ident: 1499_CR31 publication-title: J. Appl. Math. contributor: fullname: H Cheng – volume: 27 issue: 07 year: 2017 ident: 1499_CR13 publication-title: Int. J. Bifurc. Chaos doi: 10.1142/S0218127417501085 contributor: fullname: Z Jiang – volume: 2017 issue: 1 year: 2017 ident: 1499_CR38 publication-title: Adv. Differ. Equ. doi: 10.1186/s13662-017-1426-5 contributor: fullname: W Lv – volume: 78 start-page: 921 issue: 2 year: 2014 ident: 1499_CR33 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-014-1486-y contributor: fullname: T Zhang – volume: 8 start-page: 55 issue: 1 year: 1979 ident: 1499_CR5 publication-title: J. Math. Biol. doi: 10.1007/BF00280586 contributor: fullname: F Brauer – volume: 292 start-page: 210 year: 2017 ident: 1499_CR21 publication-title: Appl. Math. Comput. contributor: fullname: C Huang |
| SSID | ssj0029488 |
| Score | 2.3498156 |
| Snippet | In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate... Abstract In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the... |
| SourceID | doaj crossref springer |
| SourceType | Open Website Aggregation Database Publisher |
| StartPage | 1 |
| SubjectTerms | Analysis Difference and Functional Equations Functional Analysis Mathematics Mathematics and Statistics optimization order-1 periodic solution Ordinary Differential Equations Partial Differential Equations prey-predator model stability state-dependent impulse |
| SummonAdditionalLinks | – databaseName: DOAJ Directory of Open Access Journals dbid: DOA link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF6kJz2IT6wv9uBJCc1jn0cVSxEUDxZ6W_cV9WBS2oh_39lNIhURL15CCAsbvplh5tvHNwidEWJF4blNeCltQrQMIQWstQji7MIJw2PTvrt7NpmS2xmdrbT6CmfCWnngFriRYzz1uafO5pboMhWWGsMJ9cRwT1lbGqWyJ1Md1ZLgl90eZibYaJkVjIUjCMCYSJCk_JaFolj_j53QmGDGW2izqwzxZftH22jNVztoY0UvcBc9PcBL7V4t7j0G68rh7rg5riH837p7lbguscZzMFQCDxeoNY5db3BYecXNR43D6usyjHvRiyi2UT3voen45vF6knQtEhILhUSTcK-p9pCnTeplkLIhQaFOlIQRb7TVpc55mTpDNSWZCWTQCOdl4SnXjIIh9tGgqit_gHAmNTOCwnBAryRGSJYTbYHP6NzxUgzReQ-ZmrdKGCoyCMFUi68CfFXAV8khugqgfg0MItbxA5hWdaZVf5l2iC56k6guspa_T3n4H1MeofU8eAl4a06P0aBZvPsTqDoacxod7BNiGNVH priority: 102 providerName: Directory of Open Access Journals |
| Title | Periodic solution and control optimization of a prey-predator model with two types of harvesting |
| URI | https://link.springer.com/article/10.1186/s13662-018-1499-9 https://doaj.org/article/d670e2e5dc2c4af08c5bb745e4b7e56a |
| Volume | 2018 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1JSwMxFH64XPQgrliXkoMnZXSaZpujFhcERcSCt5htVMQZaSv-fV_SaVHUg5dAwhsG3pKXLy_5ArDHmFPdIF0my8JlzBQxpBC1diM5u_LKyvRo39W1uOizy3t-PwN0unVRvRxOKpJpok5RrcTRsNMVIp4iQNDDIqvkLMxj6skj4GL5-RRkFeiRTfXy18--5Z9E0_-jBppSy9kyLDVrQnI8NuIKzIRqFRa_MAVi72pKrzpcg4cbHK79syMTzyGm8qQ5dk5qnAZem_uVpC6JIW9osAwbHyE2Sa_fkLgDS0YfNYm7sMMo92QGiXSjelyH_tnpXe8ia55KyBwuKEaZDIabgPna5qGIlDYsMtWpkgkWrHGmNFSWubfccNaxERRa5UPRDVwawdEgGzBX1VXYBNIpjLCKozjqsmRWFYIy4xDXGOplqVqwP1GgfhszYuiEJJTQY21r1LaO2tZFC06iiqeCkcw6DdSDR93EhvZC5oEG7h11zJS5ctxayXhgVgYuTAsOJgbSTYQN__7l1r-kt2GBRudA96R8B-ZGg_ewi8uMkW0nv2rD_Mnp9c0t9nqi106QHds-Pf4EDKTQew |
| link.rule.ids | 315,783,787,867,2109,27936,27937,40913,41132,41535,41982,42201,42604,51588,52107,52246 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3JTsMwELVYDsABsYqy-sAJFNGm3nIEBCpLEQcqcTPeUjiQoKaI32fGTSoQcOASKdZEkWbxzPPYz4QcMuZUN0iXyDxzCTMZhhSg1i6SsyuvrIyX9vXvRG_Arh_5Y32Ou2p2uzctyThTx7BW4qTqdIXAbQSAehjSSs6SeaRXR8L8QXo6RVkZuGTdvvz1s28JKPL0_2iCxtxyuUKW66KQnk6suEpmQrFGlr5QBcJbf8qvWq2Tp3sYLv2Lo43rUFN4Wu87pyXMA6_1AUta5tTQN7BYAg-PGJvG628oLsHS8UdJcRm2QrlnM4qsG8VwgwwuLx7Oe0l9V0LioKIYJzIYbgIkbNsOGXLaMKSqUzkTLFjjTG5Smbe95YazjkVUaJUPWTdwaQQHi2ySuaIswhahncwIqziIgy5zZlUmUmYcABuTepmrFjlqFKjfJpQYOkIJJfRE2xq0rVHbOmuRM1TxVBDZrONAORrqOji0F7Id0sC9Sx0zeVs5bq1kPDArAxemRY4bA-k6xKq_f7n9L-kDstB76N_q26u7mx2ymKKjgK-mfJfMjUfvYQ9qjrHdjz72CVL1z78 |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1Lb9NAEF5BkCo4oFJApFDYQ08gq469Lx8hbRRoE-VApNyWfaYcsKPYFX-fGT8iKuDAxZJXY1max-5-O7PfEHLOmFN5kC6RsXAJMwWGFKDWHMnZlVdWtk37FksxX7MvG77p-5zWQ7X7kJLs7jQgS1PZXOx87EJciYt6kguBJQWAgBhSTD4kjxj2TMdsrZgeEFcB7tmnMv_62b3FqOXs_yMh2q4zs2PytN8g0o-dRZ-RB6E8IU9-ow2Et8WBa7V-Tr6tYLjy3x0d3Iia0tO-Bp1WMCf86C9b0ipSQ3dgvQQeHvE2bVvhUDyOpc3PiuKRbI1yt2bfMnCU2xdkPbv6Op0nfd-ExMHuoklkMNwEWLxtGgrkt2FIW6ciEyxY40w0mYypt9xwNrGIEK3yocgDl0ZwsM5LMiqrMrwidFIYYRUHcdBlZFYVImPGAcgxmZdRjcn7QYF619Fj6BZWKKE7bWvQtkZt62JMPqGKD4LIbN0OVPut7gNFeyHTkAXuXeaYialy3FrJeGBWBi7MmHwYDKT7cKv__cvT_5J-R45WlzN983l5_Zo8ztBPwG0z_oaMmv1dOIPtR2Pfti72CzZd0-U |
| 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=Periodic+solution+and+control+optimization+of+a+prey-predator+model+with+two+types+of+harvesting&rft.jtitle=Advances+in+difference+equations&rft.au=Wang%2C+Jianmei&rft.au=Cheng%2C+Huidong&rft.au=Liu%2C+Hongxia&rft.au=Wang%2C+Yanhui&rft.date=2018-01-25&rft.pub=Springer+International+Publishing&rft.eissn=1687-1847&rft.volume=2018&rft.issue=1&rft_id=info:doi/10.1186%2Fs13662-018-1499-9&rft.externalDocID=10_1186_s13662_018_1499_9 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1687-1847&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1687-1847&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1687-1847&client=summon |