پديد آورنده :
خليلي، اميرحسين
عنوان :
پايداري و ناپايداري يك شبكه عصبي با اتصالات جهان- كوچك تحريكي و بازدارنده
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
[يازده]، ۸۲ص.: مصور، نمودار
استاد راهنما :
رسول عاشقي
استاد مشاور :
محمدرضا احمدزاده
توصيفگر ها :
انشعاب , پايداري سراسري وابسته به تاخير , نظريه اختلال ماتريس , نظريه ميدان - ميانگين
استاد داور :
بهناز عمومي، مريم ذكري
تاريخ ورود اطلاعات :
1397/10/26
چكيده انگليسي :
Stability and instability of a neuron network with excitatory and inhibitory small world connections Amir Hosein Khalili a khalili@math iut ac ir December 30 2018 M Sc Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Rasoul Asheghi r asheghi@cc iut ac irAdvisor Dr Mohamadreza Ahmadzadeh Ahmadzadeh@cc iut ac ir2010 MSC 92B20 34K20 35B32 Keywords Bifurcation Delay dependent global stability Matrix perturbation theory Mean field theory Small world network Abstract This M Sc thesis is based on the following paper Dongyuan Yu Xu Xu Jing Zhou Eric Li Stability and instability of a neuron network with excitatory and inhibitory small world connections Neural Networks 89 2017 50 60 In general this study considers a delayed neural network with excitatory and inhibitory shortcuts The global stabilityof the trivial equilibrium is investigated based on Lyapunov s direct method and the delay dependent criteria are ob tained It is shown that both the excitatory and inhibitory shortcuts decrease the stability interval but a time delay canbe employed as a global stabilizer In addition we analyze the bounds of the eigenvalues of the adjacent matrix usingmatrix perturbation theory and then obtain the generalized sufficient conditions for local stability The possibility ofsmall inhibitory shortcuts is helpful for maintaining stability The mechanisms of instability and bifurcation modesare also investigated Compared with methods based on mean field theory the proposed method in 8 can guaranteethe stability of the system in most cases with random events The proposed method in 8 is effective for cases whereexcitatory and inhibitory shortcuts exist simultaneously in the network In details a small world network Newman Watts model is considered We start with a ring network of size n whereeach node is connected to its left and right hand side k nearest neighbors where k is even and k n Shortcuts 2are then added between two randomly chosen long range nodes with a small excitatory possibility p or inhibitorypossibility p No multiple connections or self connections are allowed in this model The dynamical equations aredescribed as follows n xi t xi t bij f xj t i 1 2 n 46 j 1where i 1 2 n bij Qij Rij with bij bji and bii 0 The global stability of the system is strongly related to the time delay Hence it is necessary to analyze how time
استاد راهنما :
رسول عاشقي
استاد مشاور :
محمدرضا احمدزاده
استاد داور :
بهناز عمومي، مريم ذكري
