12982

11865

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

۱۳۹۶

[هشت]، [۹۷]ص.: مصور، جدول، نمودار

حميدرضا ظهوري زنگنه

انگليسي به فارسي، فارسي به انگليسي

رسول عاشقي، رضا خوش سير

1396/08/16

كتابنامه

علوم رياضي

رياضي

ID11865

Stability and bifurcation analysis in a predator prey system with Michaelis Menten type predator harvesting Javad haddadi j1741366@gmail com 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid R Z Zangeneh hamidz@cc iut ac ir 2010 MSC 37Gxx 34C23 37Mxx Keywords Predator prey system Michaelis Menten type predator harvesting Stability Bifurca tion Phase portrait AbstractEver since the pioneering work of Lotka and Volterra who first proposed two differential equations thatdescribe the relationship between predators and prey in 1925 and 1926 respectively 1 predators andprey models have been continuously researched over the last one hundred years due to its significancein many problems 16 28 In 1919 May et al 24 proposed the following model to describe the interaction of predators andtheir prey subjected to various harvesting regimes x r1 x 1 x axy H1 K 1 y r y 1 y H 2 2 bxwhere x t and y t represent the prey and predators densities at time t respectively r1 and Kdescribe the intrinsic growth rate and the carrying capacity of the prey in the absence of predators respectively a is the maximum value at which per capita reduction rate of the prey x can attain r2 isthe intrinsic growth rate of predators bx takes on the role of a prey dependent carrying capacity forpredators and b is a measure of the quality of the food for predators H1 and H2 describe the effectof harvesting on the prey and predators respectively In this thesis we have studied the dynamics of a predator prey system where predator is provided

حميدرضا ظهوري زنگنه

رسول عاشقي، رضا خوش سير