Emergent explosive transition on ring networks with low-pass filter

Abstract

Low-pass filter plats an indispensable action in tracking and stabilizing the steady state of dynamical system via introducing an unstable degree of freedom. Even recent studies reveal condition that contributes to the explosive death, the first-order transition process to oscillation quenching remains unclear on complex dynamical networks where the low-pass filter is applied. In this paper, the role of the low-pass filter under the action of an active component on explosive transition is illustrated on a ring network. It is showed that the low-pass filter attaching to the amplifier could induce and enhance the appearance of the explosive nontrivial amplitude death behavior. While multiple dynamic behaviors including the coexistence region made up by amplitude death and complete synchronization and the coexistence region composed by amplitude death and nontrivial amplitude death arise if the attenuator is applied to low-pass filter. It is further indicated that emergent hysteresis area accompanying explosive death and the coexistence area causing by the amplifier could be adjusted via the cut-off frequency of the low-pass filter. Our result is a step forward in controlling over the induced explosive behaviors and the multistability, which is of great importance in widening our understanding on the explosive transition in various filter-based diffusively coupled biological and engineering systems.