12238

11211

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

دوازده، [120]ص.: مصور.

ص. ع. به فارسي و انگليسي

رضا مزروعي سبداني

واژه نامه

مجيد گازر، رضا خوش سير قاضياني

1395/12/04

كتابنامه

علوم رياضي

رياضي

ID11211

Bifurcations of invariant tori in predator prey models with seasonal prey harvesting Faezeh Hajializadeh f hajializadeh@math iut ac ir 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza MazrooeiSebdani mazrooei@cc iut ac ir 2010 MSC 05C15 53C42 Keywords predator prey model seasonal harvesting Bogdanov Takens bifurcation degenerateHopf bifurcation periodic orbit invariant torus homoclinic torus Abstract This thesis is an extension and generalization of the works done by Chen J Haung J Ruan Sand Wang J 7 In this paper we study bifurcations in predator prey systems with seasonal preyharvesting First when the seasonal harvesting reduces to constant yield it is shown that variouskinds of bifurcations including saddle node bifurcation degenerate Hopf bifurcation and Bogdanov Takens bifurcation i e cusp bifurcation of codimension 2 occur in the model as parameters vary The existence of two limit cycles and a homoclinic loop is established Bifurcation diagrams andphase portraits of the model are also given by numerical simulations which reveal far richer dynamicscompared to the case without harvesting Second when harvesting is seasonal described by a periodicfunction sufficient conditions for the existence of an asymptotically stable periodic solution andbifurcation of a stable periodic orbit into a stable invariant torus of the model are given Numericalsimulations including bifurcation diagrams phase portraits and attractors of Poincar e maps arecarried out to demonstrate the existence of bifurcation of a stable periodic orbit into an invarianttorus and bifurcation of a stable homoclinic loop into an invariant homoclinic torus respectively asthe amplitude of seasonal harvesting increases Our study indicates that to have persistence of theinteracting species with seasonal harvesting in the form of asymptotically stable periodic solutions orstable quasi periodic solutions initial species densities should be located in the attraction basin ofthe hyperbolic stable equilibrium stable limit cycle or stable homoclinic loop respectively for the

رضا مزروعي سبداني

مجيد گازر، رضا خوش سير قاضياني