Cluster synchronization for directed coupled inertial reaction-diffusion neural networks with nonidentical nodes via non-reduced order method

The cluster synchronization issues are investigated for directed coupled inertial reaction-diffusion neural networks (CIRDNNs) with nonidentical nodes by imposing two effective pinning control. A novel Lyapunov-Krasovskii functional (LKF) is established to directly analyze the dynamic behavior of CIRDNNs and deal with reaction-diffusion term, inertia term and coupling term. Moreover, based on different desired cluster synchronization states including a set of un-decoupled trajectories and the particular solutions of the decoupled node systems, two class of synchronization criteria in view of algebraic inequalities are derived under two different communication topologies, respectively. Finally, two typical examples are given to verify the theoretical results.