Behavior of a network of heterogeneous Liénard systems under strong output coupling

Abstract

In this paper, to participate in the understanding of a biological system, we analyze the synchronous and oscillatory behavior of coupled Liénard systems. In particular, we will consider a network of heterogeneous Liénard systems under output diffusive coupling to take into account two fundamental characteristics of a biological system. The key idea in this work is to emphasize the role of a network, which introduces an emergent behavior that each individual element approximately follows, hence making elements approximately synchronize. The intuition comes from a series of developments recently made in the name of ‘blended dynamics,’ and thus, the common philosophy of ‘blended dynamics’ approach enables us to illustrate a biological phenomenon that collective behavior is preserved even when there are some malfunctioning elements.