Explosive death in nonlinear oscillators coupled by quorum sensing

Abstract

Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we explore the dynamics of nonlinear oscillators, specifically Stuart-Landau oscillators and Rayleigh oscillators, interacting globally through dynamical agents in the surrounding environment modeled as a quorum sensing interaction. The system exhibits the typical continuous second-order transition from oscillatory state to death state, when the oscillation amplitude is small. However, interestingly, when the amplitude of oscillations is large we find that the system shows an abrupt transition from oscillatory to death state, a transition termed "explosive death". So the quorum-sensing form of interaction can induce the usual second-order transition, as well as sudden first-order transitions. Further in case of the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. This emergent regime of hysteresis widens with increasing strength of the mean-field feedback, and is relevant to hysteresis that is widely observed in biological, chemical and physical processes.

References in corpus (10)

• Explosive Synchronization Transitions in Scale-free Networks
• Amplitude Death: The emergence of stationarity in coupled nonlinear systems
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• General mechanism for amplitude death in coupled systems
• Collective Atomic Recoil Laser as a synchronization transition
• Amplitude death in complex networks induced by environment
• Explosive oscillation death in coupled Stuart-Landau oscillators
• Synchronization of oscillators coupled through an environment
• Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling
• Environment induced Symmetry Breaking of the Oscillation-Death State

Cited by in corpus (5)

• Dynamic interaction induced explosive death
• Amplitude chimera and chimera death induced by external dynamical agents
• Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions
• Resilience of networks of multi-stable chaotic systems to targetted attacks
• Interspecies evolutionary dynamics mediated by public goods in bacterial quorum sensing