Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with...

In this paper we investigate cluster collective behaviors aroused by epidemic spread in a patchy population via feedback pinning control strategy. We construct a class of complex network system combined with states feedback behavior synchronization network systems and epidemic spread constant population systems with patch dispersal. In which the dispersal effect among patches are included in the susceptible systems, as well as considering the contact willing function for each patch, determined by the disease's information and individuals' behaviors, as the added cofactor before bilinear incidence. On the one hand, we derive conditions about the global asymptotical stability of disease-free equilibrium, and the existence of positive equilibrium. On the other hand, we design states feedback controllers related with the patch disease information to achieve cluster behaviors synchronization. By using the Lyapunov stability analysis method, the global asymptotical stability of the positive equilibrium is discussed, and meanwhile, the criteria for cluster collective behaviors are obtained. Numerical simulations are performed to support our theoretical results.