تجزيه و تحليل انشعاب دستگاه هاي شكار- شكارچي در مدل هاي زيستي مختلف

چكيده انگليسي :

The bifurcation analysis of the predator prey systems in various biological models Haniyeh Fattahpour h fattahpour@math iut ac ir December 19 2018 Ph D Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Hamidreza Zohouri Zangeneh hamidz@cc iut ac irAdvisor Dr Nemat Nyamoradi nyamoradi@razi ac ir2000 MSC 37N25 37L10 37L15 35B10 Keywords Ordinary differential equation Delay differential equation Beddington DeAngelis func tional response Michaelis Menten type functional harvesting specialist and generalist predator Coral reef stability bifurcation Abstract Mathematical models are important tools for analyzing ecological models The dynamic relationship betweenprey and predators is one of the prevailing issues in mathematical ecology 2 5 19 23 25 38 46 50 Themost common method of modelling ecological interactions consists of two differential equations with simplecorrespondence between the consumption of prey by the predator and the population s growth The traditionalpredator prey models have been studied extensively 7 10 13 30 31 Yodziz 52 proposed the following modelto describe the interaction of predators and their prey P f P U F P U U U G P U where P t and U t represent the prey and predators densities at time t respectively the function f f P characterizes the growth rate of the prey population in the absence of predator The most crucial element inthese models is the functional response the term that describes the rate at which the prey is consumed bya predator The function F P U describes the predator s functional behavioral response and the functionG P U describes the predator s numerical response There have been several famous functional response type Holling types I III 26 27 Hassell Varley 24 Beddington DeAngelis 4 15 the Crowley Martin 12 and the ratio dependence 3 35 Among them theHolling type I III were labeled prey dependent and the other types which consider the interference amongpredators were labeled predator dependent by Arditi and Ginzburg 3 However prey dependent func tional responses fail to model the interference among predators or although less likely the cooperation whichis sometimes achieved and have been facing challenges from biologists and physiologists 1 3 22 29 35 Recently predator dependent type models have received much support from theoretical and empirical workin biology Prey predator models with predator dependent functional responses can provide better descriptions of preda tor feeding than prey dependent functional responses over a range of predator prey abundances as notedby Skalski and Gilliam in 44 and in some cases the Beddington DeAngelis functional response performedbest The original type prey predator model with the Beddington DeAngelis functional response has beenproposed and well studied This model has the form P P r P a bP cU P U k 1 U a bP cU dU P UMotivated by this system many scholars have proposed and studied models consisting of ordinary or functionaldifferential equations incorporating the Beddington DeAngelis functional responses For instance Hwang 31 32 showed that the interior equilibrium of the above system is globally stable provided that it is locallyasymptotically stable Further he obtained sufficient conditions for the uniqueness of limit cycles of the system In recent decades it has been demonstrated that complex dynamics can appear in continuous time modelswith three or more species 20 37 42 45 47 and specifically that nonlinear dynamics including cycles andchaos can occur in such biological systems Although a direct link between the predators and preys cannot

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تجزيه و تحليل انشعاب دستگاه هاي شكار- شكارچي در مدل هاي زيستي مختلف

معادلات ديفرانسيل عادي , معادلات ديفرانسيل تاخيري , تابع پاسخ بدينگتون - دي آنجليس , تابع برداشت مايكليس -منتن , شكارچي خاص و عام , تپه هاي مرجاني , پايداري , انشعاب