具有时滞的食饵-捕食者模型的分支分析(英文)-豆柴文库

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具有时滞的食饵-捕食者模型的分支分析(英文)
Introduction：
Predator–preyinteractionsareoneofthefundamentalecologicalprocessesthatinfluencethedynamicsanddistributionofspeciespopulations.Thebasicpredator-preymodelisoneofthemostextensivelystudiedecologicalmodelswithanextensivemathematicalanalysis.Thebasicpredator-preymodelassumesadirectrelationshipbetweenthepredatorandthepreywithoutanytimedelayorfeedbackeffects.However,inreality,thereexistsatimelaginthepreyconsumptionbythepredator,whichcanleadtodynamicalcomplexitiesinthepredator-preysystem.Inthispaper,wewillexplorethebranchanalysisofthepredator-preymodelwithatimedelayinpreyconsumptionbythepredator.
ModelDescription：
Letusconsiderapredator-preymodelwithatimedelayinthepreyconsumptionbythepredator.Themodelcanberepresentedbythefollowingequations:
dx/dt=ax(t)-bx(t-τ)y(t-τ)
dy/dt=cy(t)-dy(t)x(t)
wherex(t)andy(t)representthepredatorandpreypopulationdensities,respectively,andτdenotesthetimedelay.Theparametersa,b,c,anddrepresentthegrowthratesandinteractionstrengthsinthepredator-preysystem.
BranchAnalysis：
Thebranchanalysisisusedtostudythestabilityandbifurcationbehaviorofthepredator-preymodelwithatimedelayinthepreyconsumptionbythepredator.ThestabilityoftheequilibriumpointsisdeterminedbytheeigenvaluesoftheassociatedJacobianmatrix.Thebifurcationanalysisinvolvestheinvestigationofthechangesinthestabilityoftheequilibriumpointsastheparametersinthemodelarevaried.
Usingthebranchanalysis,wefoundthatthepredator-preymodelwithatimedelayinthepreyconsumptionbythepredatorcanexhibitavarietyofdynamicalbehaviors.Dependingontheparametersinthemodel,thesystemcanexhibitstablelimitcycles,unstablelimitcycles,andcoexistingattractors.Thesystemcanalsoexhibitcomplexdynamicalbehaviorssuchaschaosandhysteresis.
Conclusion：
Inthispaper,wehaveexploredthebranchanalysisofthepredator-preymodelwithatimedelayinthepreyconsumptionbythepredator.Ouranalysisrevealedthatthepredator-preysystemcanexhibitavarietyofdynamicalbehaviors,includingstablelimitcycles,unstablelimitcycles,andcoexistingattr