Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

Abstract

In this paper, the problem of exponential cluster synchronization of general hybrid-coupled impulsive dynamical networks with internal delay and delayed coupling is investigated. A more general delayed coupling term including different transmission delay and self-feedback delay is taken into account. By using average impulsive interval approach and the analysis technique, some novel globally exponential cluster synchronization criteria are derived analytically. It is noted that the internal delay, transmission delay and self-feedback delay are all time-varying and can be different from each other, the inner connecting matrices are not demanded to be diagonal and the coupling matrices are not restricted to be symmetric or irreducible, more consistent with the realistic networks. Particularly, it is shown that the derived cluster synchronization criteria are simultaneously applicable for studying general delayed dynamical networks with synchronizing impulses or desynchronizing impulses. Numerical examples are finally given to illustrate the effectiveness of the obtained theoretical results.