1 Hierarchical control based output synchronization of coexisting attractor networks *

This paper introduces the concept of hierarchical control based output synchronization of coexisting attractor networks. Under the new framework, each dynamical node is made passive through intra control at first, which is only related with node dynamics itself. Then each dynamic node is looked as one agent, and on account of that, the solution of output synchronization of coexisting attractor networks is transformed into multi-agent consensus problem, which can be made possible in helps of local interaction among each agent’s neighbors, this distributed working ways of coordination is named as inter control action, and it is contributed by its nearest neighbors, and can be only determined by the topology structure of the network. As long as the network is connected and balanced, network output synchronization will come true via synergy of intra control and inter control actions, which can be proved theoretically through building of a composite Lyapunov function from its individual node ones. In case of completeness, we give several illustrative examples, where the coexisting network consists with 5 identical Newton-Leipnik nodes, their topology structure varies from star connection, ring connection to chain connection, which ar