De Lellis Pietro, di Bernardo Mario, Garofalo Franco
Department of Systems and Computer Engineering, University of Naples Federico II, Naples, Italy.
Chaos. 2008 Sep;18(3):037110. doi: 10.1063/1.2944236.
Two local adaptive strategies for the synchronization of complex networks are discussed in this paper. One, termed as vertex-based, uses local adaptive coupling gains at each node in the network. The other, named edge-based, associates to each edge in the network an adaptive coupling gain, determined solely on the basis of local information. The global asymptotic stability of the synchronous evolution is proven for both strategies using appropriate Lyapunov-based techniques. The effectiveness of the adaptive methodologies presented in the paper is shown via two representative examples: adaptive consensus and the adaptive synchronization of a network on N coupled Chua's circuits.
本文讨论了复杂网络同步的两种局部自适应策略。一种称为基于顶点的策略，它在网络中的每个节点使用局部自适应耦合增益。另一种称为基于边的策略，它为网络中的每条边关联一个自适应耦合增益，该增益仅根据局部信息确定。使用适当的基于李雅普诺夫的技术证明了这两种策略的同步演化的全局渐近稳定性。通过两个代表性示例展示了本文提出的自适应方法的有效性：自适应一致性和N个耦合蔡氏电路网络的自适应同步。
