Quorum sensing in populations of spatially extended chaotic oscillators coupled indirectly via a heterogeneous environment

TL;DR

This paper explores how populations of spatially distributed chaotic oscillators exhibit complex synchronization behaviors through an indirect, heterogeneous environmental coupling, revealing a novel quorum sensing transition influenced by population density.

Contribution

It introduces a new understanding of quorum sensing in spatially extended chaotic oscillators with heterogeneous environmental coupling, including a non-traditional transition pattern and a predictive stability analysis.

Findings

Identification of various synchronization states including oscillation death and phase synchronization

Discovery of a non-traditional quorum sensing transition influenced by population density

Application of master stability function to predict synchronization, confirmed by numerical simulations

Abstract

Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here, we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states such as oscillation death, phase synchronization, and complete synchronized oscillation as well as their transitions were found. More importantly, we uncovered a non-traditional quorum sensing transition: increasing the density would first lead to collective oscillation from oscillation quench, but further increasing the population density would lead to degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. Further more, by treating the indirectly coupled systems effectively to the system with directly local coupling, we applied the master stability function approach to predict the occurrence of the complete synchronized oscillation, which were in agreement with the direct numerical simulations of the full system. The possible candidates of the experimental realization on our model was also discussed.