一类耦合动态网络的自适应性渐近同步与稳定(英文)

鉴于许多大规模复杂动态网络都显示出某种群体性同步运动,何光明与杨静宇讨论了非线性耦合动态网络的自适应同步,通过运用微分方程中的不变原理建立自协调反馈强度的线性反馈因子,发展了一种促进相关系统同步的方法,并通过数值实验说明了方法的有效性。继续何光明与杨静宇的工作,研究一类具有非均匀耦合强度的非线性耦合动态网络的自适应渐近同步与自适应渐近稳定。给出非线性耦合动态网络自适应渐近同步与自适应渐近稳定的定义,并运用微分方程中的李雅普洛夫方法建立系统实现自适应渐近同步的充分条件与实现自适应渐近稳定的充分条件。最后通过数值实验验证理论。

Adaptive asymptotical synchronization and stabilization in one kind of coupled dynamical network

Note that many large-scale complex dynamical networks display a collective synchronization motion.Recently,adaptive synchronization in non-linearly coupled dynamical networks has been studied by He and Yang.By using the invariance principle of differential equations to construct linearly feedback controllers with dynamical updated feedback strengths,they develope a method to make the dynamical network synchronize.The present work continues the study of He and Yang,investigating the adaptive asymptotical asymptotical synchronization and the adaptive stabilization in one kind of coupled dynamical networks with non-uniform coupling strength.The author propos the definitions of adaptive asymptotical synchronization and adaptive asymptotical stabilization for the dynamical network addressed.And the author establish sufficient conditions for both the synchronization and the stabilization of the network.Numerical examples are also given to verify the theoretical results.