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Aging transition by random errors.

Zhongkui Sun1, Ning Ma1, Wei Xu1

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Random errors can control the robustness of coupled nonlinear oscillators. Noise intensity and variance can enhance system stability, offering a new method for managing aging transitions in practical oscillator systems.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Statistical physics

Background:

  • Coupled nonlinear oscillators exhibit complex behaviors.
  • Hopf bifurcations mark transitions in dynamical systems.
  • Measurement errors can significantly impact system dynamics.

Purpose of the Study:

  • To investigate the impact of random errors on oscillating behaviors in a coupled nonlinear oscillator.
  • To explore how different noise types (uniform and normal) affect system robustness.
  • To identify methods for controlling aging transitions in oscillator systems.

Main Methods:

  • Theoretical analysis of a prototypical coupled nonlinear oscillator.
  • Numerical simulations employing uniform and normal random noise.
  • Analysis of the Stuart-Landau model near a Hopf bifurcation.

Main Results:

  • Uniform random noise: Increasing noise intensity enhances system robustness.
  • Normal random noise: Increasing variance enhances robustness above a certain aging transition probability threshold.
  • Normal random noise: Decreasing variance enhances robustness below the threshold.

Conclusions:

  • Random errors can be utilized to control the robustness and aging transition critical value in coupled oscillator systems.
  • The findings offer insights into managing complex dynamics in systems with active and inactive oscillators.
  • This study provides a novel approach to stabilizing nonlinear oscillator systems through controlled noise application.