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arXiv · 2512.22445

Universality classes of chaos in non Markovian dynamics

Vinesh Vijayan
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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.

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Vinesh Vijayan. 2025-12-27. Universality classes of chaos in non Markovian dynamics. https://arxiv.org/abs/2512.22445

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