Inducing amplitude death via pinning control

Abstract

The amplitude death (AD) phenomenon is an important dynamical behavior. Seeking the generation condition that induces AD has been an active and popular research field over the last two decades. In this paper, we report the emergence of AD in the identical coupled system with different network topologies through the pinning control. Using the negative self-feedback as the controllers to pin the network nodes, the critical condition that AD appears can be obtained theoretically. Moreover, the numerical scenarios, such as a single oscillator, two coupled oscillators, and coupled oscillators in regular and complex networks, have also been carried out to validate the effectiveness of the strategy, which coincides with the theoretical predictions. We show that, although the high degree nodes should be pinned preferentially to reach better efficiency for complex networks, the location (or significance) of nodes in network is more noteworthy than the degree of nodes for some regular networks. Our findings therefore provide a possibility to induce AD in coupled systems with different network topologies whose internal parameters and coupling schemes cannot be modified.

Graphical abstract