Noise-induced chaos: A conditioned random dynamics perspective

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.