Quorum sensing in populations of spatially extended chaotic oscillators coupled indirectly via a heterogeneous environment. (English) Zbl 1381.34076
Summary: 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 element communicates with each other is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here, we investigate 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 are explored. In particular, we uncover a non-traditional quorum sensing transition: increasing the population density leads to a transition from oscillation death to synchronized oscillation at first, but further increasing the density results in degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization.
The underlying mechanism of this finding is attributed to the dual roles played by the population density. What’s more, by treating the environment as another component of the oscillator, the full system is then effectively equivalent to a locally coupled system. This fact allows us to utilize the master stability functions approach to predict the occurrence of complete synchronization oscillation, which agrees with that from the direct numerical integration of the system. The potential candidates for the experimental realization of our model are also discussed.
MSC:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
Keywords:
synchronization transition; environment coupling; population density; master stability functionReferences:
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