Advanced Mathematical Models & Applications

In the paper we study the identical synchronization of drive-response neural networks of n reaction diffusion systems of Hindmarsh-Rose type with arbitrary topological structures. First the definition of the identical synchronization between the drive-response complex networks of n reaction-diffusion systems and some preliminary knowledge is given. By using the Lyapunov theory and LaSalle’s invariance principle, we design some schemes to construct the response networks to achieve the desired synchronization. We propose a nonlinear adaptive controller in order to achieve the desired synchronization of these two networks of the same node dynamics. At the end of the paper two numerical examples are given to verify the simulation results and to demonstrate the effectiveness of the proposed method.