仅有x-分量耦合的非恒同Lorenz系统的渐近同步

Asymptotic Synchronization of the Coupled Nonidentical Lorenz Equations with the x-component Coupling

考虑外部耦合格式为n×n阶实对称不可约,行和为零且对角线以外的元素非正的矩阵,内部耦合格式为仅有x-分量参与耦合的非恒同Lorenz格点系统的渐近同步.运用Lyapunov稳定性理论讨论系统解的一致有界耗散性.并在此基础上采用Cauchy-Schwarz不等式证明当耦合强度足够大时仅有x-分量参与耦合的非恒同Lorenz格点系统的解出现渐近同步,即系统解的任意两个对应分量的差在时间趋向于无穷时是一个小的有界量.

The asymptotic synchronization in a lattice of xi-coupled nonidentical Lorenz equations is considered, the external coupling matrix is an n × n irreducible symmetric real matrix having zero row sums and nonpositive off-diagonal elements. The uniform bounded dissipativeness of the coupled Lorenz systems is discussed by Lyapunov stability theory. Under this condition, applying Cauchy-Schwarz inequality to prove that asymptotic synchronization occurs for the coupled Lorenz systems with x-component coupling provided the coupling coefficient is sufficiently large. That is, the difference between any two components of a solution is bounded by the quantity O（ε） as t →∞, where ε is the maximal deviation of parameters of nonidentical Lorenz Equations.