پديد آورنده :
نريماني، هاجر
عنوان :
ديناميك هاي برخي مدل هاي اكولوژي و اپيدميولوژي زمان - گسسته
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
علوم رياضي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
[ده]،85ص.: مصور
يادداشت :
ص.ع.به فارسي و انگليسي
استاد مشاور :
رضا خوش سيرقاضياني
تاريخ نمايه سازي :
11/12/93
استاد داور :
حميدرضا ظهوري زنگنه، محمدرضا رئوفي
چكيده انگليسي :
Dynamics of Some Discrete Time Models in Ecology and Epidemiology Hajar Narimani h narimani@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Majid Gazor mgazor@cc iut ac ir Advisor Dr Reza Khoshsiar Ghaziani xx 2010 MSC 34D08 37D45 37H20 92D30 92D40 Keywords Ricardo Malthus Model SIS Model Discrete Time Stability Manifold Bifurcation Normal Form Chaos Liapunov Exponent AbstractThis thesis is concerned to dynamics of some models in ecology and epidemiology In fact we considera discrete time prey predator Ricardo Malthus model and also a SIS discrete time epidemic model For the Ricardo Malthus model we investigate stability of positive xed point period doubling bi furcation Neimark Sacker bifurcation resononce 1 2 bifurcation and resononce 1 3 bifurcation Weintroduce normal forms of these bifurcations Then we consider SIS epidemic model We study sta bility of equlibria resononce 1 2 and resonance 1 4 bifurcations and then we compute normal forms ofbifurcations To illustrate our result we simulate bifurcation diagrams and phase portraits for someparameters Also by computing the Lyapunov exponents we observe the chaotic dynamics in thesetwo models In recent years the discrete dynamical models are widely investigated The reasons are that manythe discrete models are more realistic than the continuous models For example in epidemic mod els since the epidemic statistics are compiled from given time intervals and not continuously Suchdiscrete models not only study with good accuracy the behavior of the continuous models but alsoassess the e ect of larger time steps It is well known for the discrete epidemic models the mainresearch subjects include the computation of the basic reproduction number the local stability andglobal stability of the disease free equilibrium and endemic equilibrium the extinction persistenceand permanence of the disease bifurcations and chaos phenomena of models etc Many important
استاد مشاور :
رضا خوش سيرقاضياني
استاد داور :
حميدرضا ظهوري زنگنه، محمدرضا رئوفي
