پديد آورنده :
آقائي، فاطمه
عنوان :
بررسي پايداري حالت همگام در شبكه اي از سيستم هاي آشوبناك
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده فيزيك
صفحه شمار :
[هشت]، 89ص.: مصور، جدول، نمودار
يادداشت :
ص.ع. به فارسي و انگليسي
استاد راهنما :
كيوان آقابابايي ساماني
استاد مشاور :
فرهاد شهبازي
توصيفگر ها :
ديناميك , خمينه ي همگام سازي , پارامتر جفت شدگي بهنجار , تابع پايداري اصلي
تاريخ نمايه سازي :
11/9/91
استاد ممتحن :
داخلي: مجتبي اعلايي
تاريخ ورود اطلاعات :
1396/09/21
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Stability of Synchronous State in Networks of Chaotic Systems Fateme Aghaei Abchouyeh f aghaei@ph iut ac ir Date of submission 2012 08 15 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianSupervisor Dr Keivan Aghababaei Samani samani@cc iut ac irAbstractOrdinary differential equations are introduced as continuous time dynamical systems at thebegining of the thesis Distinction of fixed points and their stability are necessary steps fordetermining behavior of systems There are two types of ordinary differential equations linearand nonlinear Most nonlinear differential equations are not solved analytically Linear systemscan be broken down into parts then each part can be solved separately and finally recombinedto obtain the answer but nonlinear systems can not it is the main difference between linearand nonlinear systems We have tried to use a geometrical method for studying of qualitativebehavior of linear systems in phase space Then the method have been expanded to nonlinearsystems for determine their behavior near the fixed points to find general schem in phase space In addition numerical methods are used to show oscillators trajectories in phase space Afterthat chaotic dynamical systems are described These oscillators have strange attractors theyare very sensitive in initial conditions and their irregularities are because of their nonlinear dy namics without any random term in their equations A system can include the features when ithas at least one negative Lyapunov exponent and one positive Lyapunov exponent Thereforecontinuous time chaotic oscillators are three dimensional at least Then we have studied syn chronization of chaotic oscillators as a collective behavior and have shown that the oscillatorscould be coupled in networks We can define time average between similar events as averageperiod of a chaotic oscillator and phase is defined corresponding their trajectories zero Lya punov exponent in phase space When oscillators affect on each other in networks a simplestway to quantify coherence in a networks is to use order parameters At last stability of completesynchronization in networks of chaotic systems is studied In the synchronous subspace that istermed synchronization manifold oscillators dynamical variables are equal Synchronizationcan be observed in physical universe if the manifold be stable with respect to perturbationsin the transverse subspace The Master Stability Function MSF that is the largest transverseLyapunov exponent of the synchronization manifold measures the exponential rate of an in finitesimal perturbation in the transverse subspace A necessary condition for synchronizationto occur is that the MSF be negative and corresponding normalized coupling parameters fallin the negative region of the MSF Previously stability of complete synchronization has beenstudied for networks that summation of elements of each coupling matrix s row is zero Wehave proved complete synchronization can be stable in networks that summation of elementsof each coupling matrix s row is constant then we have used MSF method for these types Keywords Dynamic Chaos Synchronization Synchronization manifold Normalized coupling parame ters Master Stability Function
استاد راهنما :
كيوان آقابابايي ساماني
استاد مشاور :
فرهاد شهبازي
