پديد آورنده :
اعتصامي، مريم
عنوان :
انشعابات در معادلات ديفرانسيل تاخيري و كاربردهاي آن در مدل هاي تعاملي تومور و سيستم ايمني
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
ده،79ص.: مصور
استاد راهنما :
رضا مزروعي سبداني
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
انشعاب هاپف , انشعاب بوتين , انشعاب هاپف - هاپف , تعامل بين تومور و سيستم ايمني
تاريخ نمايه سازي :
1394/10/26
استاد داور :
رضا خوش سير قاضياني، محمدرضا رئوفي
چكيده انگليسي :
Bifurcations in Delay Di erential Equations and Applications to tumorand Immune System Interaction Models Maryam Etesami m etesami@math iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Reza Mazrooei Sebdani mazrooei@cc iut ac ir Advisor Dr Majid Gazor mgazor@cc iut ac ir 2010 MSC 37N25 37G15 37G05 34C23 Keywords delay di erential equations Hopf bifurcation Bautin bifurcation Hopf Hopf bifur cation tumor immune system interaction Abstract This thesis is an extension and generalization of the work done by Ping Bi and Shigui Ruan Bifurcation in delay di erential equations and applications to tumor and immune system interactionsmodels 5 In this thesis we consider a two dimensional delay di erential system with two delays By studingequlibirium points the stability regions for some di erent parameters of these points can be obtainedand by analyzing the distribution of eigenvalues linear stability of the equilibria and existence ofHopf Bautin and Hopf Hopf bifurcations are obtained in which the time delays are used as thebifurcaion parameter In this study we assume that our system has one positive equlibirium althoughit could have multipe positive equlibirium For the sake of simplicity these bifurcations are consideredfor equal delays Then we compute the center manifold and normal form of these bifurcations byusing of normal form we can use the xed point of poincar map to show existence of periodic ecycle in each bifurcation The stabilty of limit cycle corresponding to the stability of xed pointof poincar map General formula for the direction period and stability of the bifurcated periodic esolutions are given for codimension two bifurcations including Hopf bifurcation Bautin bifurcationand Hopf Hopf bifurcation It is worth mentioning that in this thesis Bautin bifurcation is assumedas a one codimention bifurcation and it is because of Bautin bifurcation is obtained by degenerating
استاد راهنما :
رضا مزروعي سبداني
استاد داور :
رضا خوش سير قاضياني، محمدرضا رئوفي
