Bounded synchronisation of a time-varying dynamical network with nonidentical nodes

This paper investigates the global bounded synchronisation problem of complex dynamical networks of coupled nonidentical nodes with general time-varying topology through the Lyapunov function and graph theory. Several sufficient conditions in form of scalar inequalities are established so that the global bounded synchronisation of the general dynamical network can be evaluated by the stability of a linear time-varying system and the boundedness of a nonlinear function, both associated with the dynamics of nonidentical nodes. These analytical results are simple yet generic, without assuming the symmetry coupling configuration matrix or calculating their eigenvalues. They can be used to explore synchronisation issues of various complex networks. Numerical simulations show their effectiveness.