{"title":"Dynamics of a plant-herbivore model with a chemically-mediated numerical response","authors":"Lin Wang, James Watmough, Fang Yu","doi":"10.5206/mase/11067","DOIUrl":null,"url":null,"abstract":"A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modifiednumerical response. This numerical response accounts for the reduction in the her-bivore's growth and reproduction due to chemical defenses from plants. It is shownthat the system exhibits very rich dynamics including saddle-node bifurcations, Hopfbifurcations, homoclinic bifurcations and co-dimension 2 bifurcations. Numerical sim-ulations are presented to illustrate the occurrence of multitype bistability, limit cycles,homoclinic orbits and heteroclinic orbits. We also discuss the ecological implicationsof the resulting dynamics.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in applied sciences and engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5206/mase/11067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modifiednumerical response. This numerical response accounts for the reduction in the her-bivore's growth and reproduction due to chemical defenses from plants. It is shownthat the system exhibits very rich dynamics including saddle-node bifurcations, Hopfbifurcations, homoclinic bifurcations and co-dimension 2 bifurcations. Numerical sim-ulations are presented to illustrate the occurrence of multitype bistability, limit cycles,homoclinic orbits and heteroclinic orbits. We also discuss the ecological implicationsof the resulting dynamics.