Center Manifold of infinitely Coupled differential equation

• Main Authors: Yi Ching Li, 李意清
• Other Authors: Chang Whei-Ching
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/55924941236471679527

碩士 === 淡江大學 === 數學學系 === 88 === Consider an array of Chua’s equation with diffusing coupling and Neumann boundary condition : u’k = ▀ (zk — f(u’k)) + D(uk-1 — 2uk — uk+1 ) (1) z’k = uk — zk + wk w’k = - ▀ z’k where k = 0 , 1 , ….. , l , u0(t) = u-1(t) , ul(t) = ul+1(t) and D > 0 is the coupling strength . A series of change of variable was used to transform equation (1) to the following : z’ = ▀ (u — z + w) w’ = - ▀ ▀z (2) ▀ ’ = 0 u’ = v v’ = av + b(z — f(u)) Then the theory of Center manifold was used to analyze the equation (2) . We have conclude that the stable dimension of the linearization of the vector field at each equilibrium varies from 1 to 3 as the value of the first derivative of the nonlinear function f(u) at the corresponding equilibrium point varies . Numerical simulation were also performed to show that the solutions of the finitely coupled Chua’s equation synchronized in every cases which is different from other studies that showed the existence of traveling wave solution . One observation is that the time it took for the solution to synchronize depends on the number of coupling . 1. 核心流形 …………………………………………...1 1.1 廣義核心流形 ………………………………….1 1.2 局部核心流形 ………………………………….4 2. Chua’s 方程式 ……………………………………10 3. 耦合方程組之研究………………………………….22 3.1 Chua’s 方程式之耦合與核心流形之計算 …22 3.2 數值模擬 ………………………………………28 4. 參考文獻…………………………………………….46