Bipartite quasi synchronization of stochastic delayed cooperation–competition networks with gain-waving intermittent control

Abstract

Given the cooperation and competition bi-directional mechanisms between subsystems, this paper aims at addressing bipartite quasi synchronization (BQS) of stochastic delayed cooperation–competition networks (SDCNs). We propose a gain-waving intermittent control policy, that includes more of the existing works, to assist the BQS, in an effort to cope with external interferences and the possibility of actuator damage caused by rapid switching. Intermittent gain is to be quantized legitimately via the postulate of waving average gain. Within this context, novel Lyapunov inequalities concerning bounded waving gain and unbounded one are advanced to ensure the BQS of SDCNs in conjunction with graph theory, since the present differential inequalities are incapable of being inoperative. Then we develop two kinds of BQS criteria and the bounds for the BQS error are estimated where the scenarios of bounded waving gain and unbounded one are involved separately. Besides, corresponding criteria about complete bipartite synchronization are presented and several design methods of gain-waving intermittent control are introduced by specific examples. Finally, the validity of the theoretical results is examined by an application on Chua’s circuit with numerical simulations being shown.