پديد آورنده :
يوسفي، زهرا
عنوان :
الگوريتم هاي عددي در آناليز انشعاب هاي سيستم هاي ديناميكي پيوسته با استفاده از MATCONT
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
دوازده، 119ص.: مصور، جدول، نمودار
يادداشت :
ص.ع. به فارسي و انگليسي
استاد مشاور :
رضا خوش سير
توصيفگر ها :
نرم افزار انشعابي , امتداد عددي
تاريخ نمايه سازي :
21/8/91
استاد داور :
محمدرضا رئوفي، رضا مختاري
تاريخ ورود اطلاعات :
1396/09/21
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Numerical Algorithms for Bifurcations Analysis of Continuous Dynamical Systems by Using MATCONT Zahra Youse z youse @math iut ac ir 15 09 2012 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 khoshsiar@sci sku ac ir 2010 MSC 34C23 37G15 37M20 65P30 Keywords dynamical system bifurcation normal form numerical continuation MATCONT Abstract Most of the real world problems can be modeled with di erential equations Systems of ODEshave applications in many elds of research including economics engineering biology chemistry and physics In the rapidly expanding eld of mathematical biology we can refer to recent researchin biochemistry 2 neuroscience 12 epidemiology 6 and immunology 15 among others Theymay be studied by using bifurcation theory and numerical methods Numerical analysis of bifurca tions requires special computations e g continuation and normal form computations construction ofauxiliary maps and computing dimensional characteristics of attractors which should be performedinteractively Therefore bifurcation analysis should combine theoretical results e cient numericalmethods and a user friendly graphical interface Bifurcation softwares are essential tools in the studyof dynamical systems From the beginning the rst packages were written in the 1970 s bifurcationsoftwares have also been used in the modelling processes In its simplest form this involves tuningthe parameters of the system in such a way that the right bifurcations with the right properties forexample a supercritical Hopf bifurcation are found at the correct place as a strong indication thatthe mathematical model behaves correctly Examples of this strategy are given in classical modellingpapers such as 17 10 and 1 More recently it is used in a systematic way in the design of dynam ical models and to determine which parameters are relevant
استاد مشاور :
رضا خوش سير
استاد داور :
محمدرضا رئوفي، رضا مختاري
