پديد آورنده :
الوند، محمد
عنوان :
استفاده از معدل گيري در مسئله انشعاب هاپف تصادفي
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
حميدرضا ظهوري زنگنه، هانس كراول
استاد مشاور :
محمدتقي جهانديده
واژه نامه :
به فارسي و انگليسي
توصيفگر ها :
معادله ديفرانسيل تصادفي , جريان براوني , مولدn- نقطه اي , ساختار كوواريانس , تجزيه چولسكي , دستگاه معادلات دوخطي مختلط
استاد داور :
بيژن ظهوري زنگنه، افشين پرورده، رسول عاشقي
تاريخ ورود اطلاعات :
1395/01/15
كد ايرانداك :
ID859 دكتري
چكيده انگليسي :
AbstractConsider a parameterized linear system in the Euclidean plane which is a rigidrotation for the critical parameter value The Hopf bifurcation is a change ofdynamics in a nonlinear perturbation of this system One form of the stochasticHopf bifurcation problem considers the perturbation of a system which under goes Hopf bifurcation with a random eld white in time One method to studythe stochastic Hopf bifurcation problem is the averaging method To apply thismethod it is necessary to nd the averaged SDE consistent with the covariancestructure obtained by classical averaging of the in nitesimal covariance of the sys tem In this thesis a constructive method is proposed to construct an SDE from acovariance structure in a Euclidean space with certain smoothness condition andits convergence is also proved The method consists of two steps rst expandingthe covariance structure in terms of a suitable completely orthonormal systemand second using the Cholesky decomposition method for the matrix containedthe coe cients of the expansion For this purpose we proved a certain general ization of the Cholesky decomposition method We use complex coordinates tosimplify our method for the special covariance structure obtained by the averag ing method in the stochastic Hopf bifurcation problem The main result describesexplicit relations between the coe cient of the original and the averaged SDE incase of polynomial di usion coe cients We have noticed that the main result isalso useful for non polynomial but analytic di usion coe cient MSC 15A23 37H10 40A30 60B10 60H10 34C29 60H35Keywords SDE stochastic averaging Brownian ow n point generator covari ance structure Cholesky decomposition system of complex bilinear equations
استاد راهنما :
حميدرضا ظهوري زنگنه، هانس كراول
استاد مشاور :
محمدتقي جهانديده
استاد داور :
بيژن ظهوري زنگنه، افشين پرورده، رسول عاشقي
