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The constructive role of random noise in sequential dynamics.

Irina Bashkirtseva1, Lev Ryashko1

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Noise constructively influences sequential dynamics in competitive systems. Random disturbances stabilize oscillations and create sequential dynamics, revealing system sensitivities.

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Area of Science:

  • Theoretical Ecology
  • Mathematical Biology
  • Complex Systems

Background:

  • The May-Leonard model describes three-population competition dynamics.
  • Understanding noise's role in ecological and cognitive systems is crucial.

Purpose of the Study:

  • To investigate the constructive role of noise in systems exhibiting sequential dynamics.
  • To analyze noise-induced phenomena in the May-Leonard model under various conditions.

Main Methods:

  • Utilized the May-Leonard model as a conceptual framework.
  • Studied three distinct cases of the model with varying equilibria and influx.
  • Applied stochastic sensitivity analysis to identify system vulnerabilities.

Main Results:

  • Random noise stabilizes stochastic oscillations when equilibria are connected by a homoclinic cycle.
  • Noise generates sequential dynamics with temporary slowdowns near stable axial equilibria.
  • An extended model with influx identified susceptible regions within limit cycles.
  • Identified scaling laws governing sequential behavior based on system parameters.

Conclusions:

  • Noise plays a constructive, not just disruptive, role in sequential dynamics.
  • The May-Leonard model, even with noise, exhibits complex behaviors like stabilization and oscillations.
  • Stochastic sensitivity analysis is effective for understanding system responses to noise.