Universality classes of chaos in non Markovian dynamics

TL;DR

This paper demonstrates that long-range memory in non-Markovian systems leads to a new universality class of chaos, breaking classical scaling laws and introducing fractional Lyapunov scaling.

Contribution

It introduces a new universality class of chaos driven by long-range memory effects, extending classical chaos theory beyond Markovian assumptions.

Findings

Breakdown of Feigenbaum universality with power law memory

Identification of a critical memory exponent separating regimes

Fractional scaling of Lyapunov exponents in the new class

Abstract

Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly assume Markovian dynamics. Here, a logistic map endowed with power law memory is used to show that Feigenbaum universality breaks down when temporal correlations decay sufficiently slowly. A critical memory exponent is identified that separates perturbative and memory dominated regimes, demonstrating that long range memory acts as a relevant renormalisation operator and generates a new universality class of chaotic dynamics. The onset of chaos is accompanied by fractional scaling of Lyapunov exponents, in quantitative agreement with analytical predictions. These results establish temporal correlations as a previously unexplored axis of universality in chaotic systems, with implications for physical, biological and geophysical settings where memory effects are intrinsic.