12011

11013

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

هشت، [91]ص.: مصور، جدول، نمودار

ص. ع. به فارسي و انگليسي

رسول عاشقي

واژه نامه

حميدرضا ظهوري زنگنه، رسول كاظمي

1395/10/28

كتابنامه

علوم رياضي

رياضي

ID11013

Existence of limit cycles and homoclinic bifurcation in a plant herbivore model with toxin determined functional response Mohaddese Raisi Sarkhoni mohaddese raisi@math iut ac ir 2016 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@cc iut ac ir 2010 MSC 34C05 92C80 Keywords Plant herbivore model Limit cycles Homoclinic bifurcation Rotated vector elds Extended planar termination principle Abstract The purpose of the present thesis is to extend the analytic results on the existence of limit cyclesand present a more complete bifurcation analysis of system 1 1 For ease of presentation we willuse K as the bifurcation parameter in our analysis and generate a bifurcation diagram similar to Fig 2 1 The main questions we intend to answer from our bifurcation analysis are the following Q1 Assume that C N is unimodal a Is there a globally de ned homoclinic bifurcation function That is can the dashed curve in Fig 2 1 be con rmed analytically b Does system 1 1 have limit cycles for d G I1 III1b That is does a limit cycle generated fromHopf bifurcation expand continually and eventually terminate at a homoclinic loop as the parametersvary Q2 What is a necessary and su cient condition on the existence of limit cycles when C N ismonotone By applying the theories of rotated vector elds and the extended planar termination principle wegive a complete answer to the above problem in an analytic way Under the assumption that C N isunimodal rstly we show that the homoclinic bifurcation curve d dhom G exists globally Secondly system 1 1 has at least one limit cycle for d G I1 III1b and no limit cycle for d G III1a

رسول عاشقي

حميدرضا ظهوري زنگنه، رسول كاظمي