Sign synchronization of coupled nonlinear systems with cooperative and competitive interactions

This paper studies various criteria for sign synchronization of coupled nonlinear systems with cooperative and competitive interactions. sign synchronization means that all states have same sign when time exceeds a threshold. When the adjacency matrix is a nonnegative matrix, Based on Kamke's theorem and Comparison theorem, we obtain some sufficient conditions such that the coupled nonlinear systems achieves unanimity. When cooperative and competitive relationships coexist and the nonlinear items are switching systems, some results of Lie bracket are used to obtain sufficient conditions for sign synchronization.