Noise-induced chaos: a conditioned random dynamics perspective

TL;DR

This paper investigates how increasing noise amplitude can induce chaos in random dynamical systems, using a novel framework that does not depend on small noise assumptions and highlights the role of escape times.

Contribution

It introduces a conditioned random dynamics approach to analyze noise-induced chaos, emphasizing escape times and Lyapunov exponents without relying on deterministic or small noise assumptions.

Findings

Chaos emerges from rapid decay of expected escape times.

Other order parameters remain stable during transition.

The approach applies to bounded additive noise in logistic maps.

Abstract

We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be analyzed in the framework of conditioned random dynamics through expected escape times and conditioned Lyapunov exponents for a compartmental model representing the competition between contracting and expanding behavior. In contrast to the existing literature, our approach does not rely on small noise assumptions, nor refers to deterministic paradigms. We find that the noise-induced transition to chaos is caused by a rapid decay of the expected escape time from the contracting compartment, while all other order parameters remain approximately constant.