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Explosive death in nonlinear oscillators coupled by quorum sensing.

Umesh Kumar Verma1, Sudhanshu Shekhar Chaurasia1, Sudeshna Sinha1

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Quorum sensing interactions in nonlinear oscillators can cause typical or abrupt transitions to a death state. Large oscillation amplitudes lead to "explosive death" and hysteresis, observed in biological and chemical systems.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Theoretical Biology

Background:

  • Biological and chemical systems display collective behavior driven by population density.
  • Cellular communication occurs via signaling molecules or dynamical agents.

Purpose of the Study:

  • To investigate the dynamics of interacting nonlinear oscillators (Stuart-Landau and Rayleigh) under quorum sensing.
  • To analyze the transition from oscillatory to death states influenced by population density and oscillation amplitude.

Main Methods:

  • Modeling global interactions of Stuart-Landau and Rayleigh oscillators.
  • Simulating quorum sensing as the interaction mechanism.
  • Analyzing system transitions based on oscillation amplitude and coupling strength.

Main Results:

  • Small oscillation amplitudes result in a continuous second-order transition to the death state.
  • Large oscillation amplitudes induce an abrupt first-order transition, termed "explosive death."
  • Hysteresis is observed in the "explosive death" regime, with coexisting oscillatory and death states.

Conclusions:

  • Quorum sensing interactions can drive both second-order and sudden first-order phase transitions in oscillator systems.
  • The emergent hysteresis is dependent on mean-field feedback strength.
  • Findings are relevant to understanding hysteresis phenomena in diverse natural and engineered systems.