Cluster synchronisation of non-linearly coupled Lur´e networks with identical and non-identical nodes and an asymmetrical coupling matrix

In this study, the cluster synchronisation problem of Lur´e networks is focused with non-linear coupling. There are both identical and non-identical nodes in the dynamical system and the coupling matrix is asymmetrical. By using the linear and non-linear negative feedback control schemes, the Lyapunov stability theorem and linear matrix inequality, sufficient conditions are obtained that guarantee the realisation of the cluster synchronisation pattern for all initial values. Numerical simulation results are also given to support the validity of the main results.