Cao Jinde, Lu Jianquan
Department of Mathematics, Southeast University, Nanjing 210096, China.
Chaos. 2006 Mar;16(1):013133. doi: 10.1063/1.2178448.
In this paper, based on the invariant principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the synchronization of almost all kinds of coupled identical neural networks with time-varying delay, which can be chaotic, periodic, etc. We do not assume that the concrete values of the connection weight matrix and the delayed connection weight matrix are known. We show that two coupled identical neural networks with or without time-varying delay can achieve synchronization by enhancing the coupling strength dynamically. The update gain of coupling strength can be properly chosen to adjust the speed of achieving synchronization. Also, it is quite robust against the effect of noise and simple to implement in practice. In addition, numerical simulations are given to show the effectiveness of the proposed synchronization method.
本文基于泛函微分方程的不变原理，针对几乎所有类型的具有时变延迟的耦合相同神经网络（其可以是混沌的、周期性的等）的同步问题，提出了一种简单、解析且严格的自适应反馈方案。我们不假设连接权重矩阵和延迟连接权重矩阵的具体值是已知的。我们表明，两个具有或不具有时变延迟的耦合相同神经网络可以通过动态增强耦合强度来实现同步。耦合强度的更新增益可以适当选择以调整实现同步的速度。此外，该方案对噪声影响具有很强的鲁棒性，并且在实际中易于实现。另外，给出了数值模拟以表明所提出的同步方法的有效性。
