Contraction approach to bipartite synchronization for a network of nonlinear systems

This paper studies the bipartite synchronization in a network of nonlinear systems. Under the assumption that the signed graph is structurally balanced and the nonlinear system satisfies a one-sided Lipschitz condition, we use contraction theory to obtain some sufficient conditions such that the network admits a bipartite synchronization solution. These conditions are described by the contractivity of lower-dimensional dynamic systems which are about the second smallest eigenvalue of signed graph. Some numerical examples are presented to illustrate the effectiveness of the obtained results.