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Area of Science:

  • * Complex Systems
  • * Nonlinear Dynamics
  • * Chaos Theory

Background:

  • * Understanding transitions to chaos in random dynamical systems is crucial.
  • * Existing literature often relies on small noise assumptions or deterministic models.
  • * The role of noise amplitude in inducing chaos requires further investigation.

Purpose of the Study:

  • * To analyze noise-induced transitions to chaos in a logistic map with bounded additive noise.
  • * To develop a framework for analyzing chaos emergence without small noise assumptions.
  • * To identify the key mechanisms driving noise-induced chaos.

Main Methods:

  • * Utilized conditioned random dynamics to analyze the system.
  • * Employed expected escape times and conditioned Lyapunov exponents.
  • * Developed a compartmental model representing competing dynamics.

Main Results:

  • * Demonstrated chaos emergence (positive Lyapunov exponent) with increasing noise amplitude.
  • * Identified a rapid decay in expected escape time from the contracting compartment as the primary driver.
  • * Observed that other order parameters remained largely constant during the transition.

Conclusions:

  • * Noise-induced transitions to chaos can be effectively analyzed using conditioned random dynamics.
  • * The study provides a novel approach independent of small noise assumptions.
  • * The decay of expected escape time is a critical indicator of chaos emergence in this model.