8483

7864

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

ده،88ص.نمودار

ص.ع.به فارسي و انگليسي

رضا مزروعي سبداني

حميدرضا ظهوري زنگنه مدار

8/11/92

رسول عاشقي، مجيد گازر

رياضي

ID7864

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Abstract Recently study on the rational systems having both a linear numerator and a linear denominator have started extensively by Gerry Ladas and colleagues This substantial research makes a strong case for studying the behaviour of rational difference equations as well as providing a great deal of information about the behaviour of rational equations with linear terms But there is no systematically study on the rational systems having quadratic terms about all of dynamics specifically chaotic dynamics A class of rational systems in the plane with quadratic terms include systems that are reducible to some second order rational difference equation with quadratic terms In developing this model it is assumed that without inter specific competition each species is modelled by the logistic map The logistic map is used to model species with non overlapping generations under the assumption that the fitness function decreases when the population density size increases Host parasitoid systems have proved fruitful models for many experimental and theoretical inves tigations in ecology and there is a rich literature on parasitoid population dynamics Host parasitoid systems have been modelled within a discrete time framework We can see discrete time models can provide more efficient computational models for numerical simulations and these results reveal richer dynamics of the discrete models compared to the continuous ones Interactions between plants and herbivores have been studied by ecologists for many decades One focus of research is the effects of herbivores on plant dynamics In contrast there is strong ecological evidence indicating that the population dynamics of plants has an important effect on the plant herbivore interactions Ecologi cal systems and their component biological populations exhibit a broad spectrum of non equilibrium dynamics ranging from characteristic natural cycles to more complex chaotic oscillations Even in simple one species models we have seen the potential for stability cycles or chaos One of the earliest applications of a discrete time model to a biological system involved two insects a parasitoid and its host The model was developed by Nicholson and Bailey and applied it to the parasitoid Encarsia formosa and the host Trialeurodes vaporarioum We will investigate stability and bifurcation of the model In particular we compute the invariant manifolds including the important center manifolds and study their bifurcation Saddle node and period doubling bifurcation route to chaos are exhibited via numerical simulations PDF created with pdfFactory trial version www pdffactory com

رضا مزروعي سبداني

حميدرضا ظهوري زنگنه مدار

رسول عاشقي، مجيد گازر