Anti-synchronization problem for cooperative-competitive multi-layer neural networks with time delays and unknown dynamics
Yanzhi Wu, Jiangping Hu, Yiyi Zhao · 2016
In this paper, an adaptive synchronization problem is considered for an array of linearly coupled reaction-diffusion neural networks with antagonistic interactions. Firstly, the interaction topology among the the neurons is modeled by a signed graph. The state evolution of a neuron in each layer of neural networks is described by a reaction-diffusion equation with Dirichlet boundary conditions. Further, the collective dynamics of the multi-layer neural networks is built as a coupled reaction-diffusion equation with both spatial diffusion coupling and state coupling. When the interactions between neurons suffer from time-varying delays, an edge-based adaptive strategy is designed to tune the coupling weights of the network and an anti-synchronization control is developed by using only local information of neighboring nodes to achieve anti-synchronization. A sufficient condition is given to guarantee anti-synchronization with the help of a Lyapunov function method and the structural balance condition. Some simulation results are provided to demonstrate the effectiveness of the proposed adaptive control strategy.