11603

10652

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

ده،84ص.: مصور.

ص.ع.به فارسي و انگليسي

حميدرضا ظهوري زنگنه

رسول عاشقي

دارد

رسول كاظمي، رضا مزروعي سبداني

1395/08/03

رياضي

ID10652

Bifurcations in prey predator models Roghaye Bagheri Vanani R Bagheri@math iut ac ir June 2016 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr H R Zohouri Zangeneh hamidz@cc iut ac irAdvisor Dr Rasuol Asheghi r asheghi@cc iut ac ir2000 MSC 05C25 20B25Keywords predator prey system Lotka Voltrra model Bifurcation theory Bogdanov Takens bifur cationAbstract This thesis is based on the following paperI Kusbeyzi O O Aybar and A Hacinliyan Stability and bifurcation in two species Predator preymodels Nonlinear Analysis Real World Applications 12 2011 377 387 AndH Zhu S A Campbell and G S K Wolkowicz Bifurcation and analysis of a predator prey systemwith nonmonotonic functional response SIAM J APPL MATH Vol 63 No 2 pp 636 682 The predator prey problem attempts to model the relationship in the populations of different speciesthat share the same environment where some of the species predators prey on the others The prey isassumed to exhibit linear growth given by a positive parameter Predator species consume preys witha nonlinear interaction with another set of parameters that determine the rate of competition betweenpredators The natural death rate of the predator is assumed to be linear and given by a negative param eter One of the earliest implementations the Lotka Volterra model serves as a starting point of moreadvanced models in the analysis of population dynamics Because of its unrealistic stability character istics stability analysis of the model and its generalizations have recently gained much attention Tounderstand the behavior of a nonlinear system one can analyze the existence and stability of equilib rium points As parameters are varied changes in the number and stability of equilibrium points leadto bifurcation The well known generalizations of the Lotka Volterra model include the addition ofpolynomial interactions non monotonic response functions time delayed and diffusion effected timedelayed non monotonic interactions Nutku has proposed a generalization where an additional cubicrather than a quadratic interaction is involved In the first part of this thesis bifurcation properties ofquadratic and cubic local and monotonic interactions are studied Consider the following prey predatorsystem x ax 1 x bxy 77 4 y cy 1 y dxy in four case we show that for a b and c d the hopf bifurcations exists The classical predator prey model with an inhibition response function was introduced in Freedmanand Wolkowicz to establish a veritable paradox of enrichment In the second part of thes we consider mxa predator prey with nonmonotonic functional response p x for system ax2 bx 1 x x rx 1 yp x p x F x y K 78 4 y y d cp x x 0 0 y 0 0

حميدرضا ظهوري زنگنه

رسول عاشقي

رسول كاظمي، رضا مزروعي سبداني