Cluster synchronisation of coupled delay reaction-diffusion systems.

This paper considers the cluster synchronisation of coupled delay reaction-diffusion systems (DRDSs). First, in light of the technique of matrix representation, we turn the cluster synchronisation of coupled DRDSs into the asymptotical stability of a transformed system. Based on this transformation and by virtue of the Lyapunov-Krasovskii functional method, we provide the sufficient conditions that ensure the cluster synchronisation for DRDSs with constant delay. The effects of spatial domain on the cluster synchronisation is shown by these sufficient conditions. Then, we deal with time-varying delay systems with reaction-diffusion term. The criterion of cluster synchronisation is presented and a brief proof is given. Finally, numerical examples are carried out to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]