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Lévy on-off intermittency.

Adrian van Kan1, Alexandros Alexakis1, Marc-Etienne Brachet1

  • 1Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France.

Physical Review. E
|June 17, 2021
PubMed
Summary
This summary is machine-generated.

We introduce Lévy on-off intermittency, a novel behavior from power-law noise near instability. This phenomenon exhibits distinct statistical and critical properties compared to Gaussian fluctuations.

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Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Complex systems

Background:

  • Intermittency is a common phenomenon in complex systems.
  • Existing models often assume Gaussian noise, limiting their applicability.
  • Understanding non-Gaussian noise effects is crucial for realistic modeling.

Purpose of the Study:

  • To introduce and characterize Lévy on-off intermittency.
  • To investigate its behavior in linear and nonlinear regimes near a pitchfork bifurcation.
  • To explore the parameter space of multiplicative α-stable white noise.

Main Methods:

  • Analytical and numerical studies of a pitchfork bifurcation with fluctuating growth rate.
  • Computation of stationary distribution using the fractional Fokker-Planck equation (Stratonovich interpretation).
  • Characterization within the (α,β) parameter space of α-stable noise.

Main Results:

  • Identification of five distinct regimes in the (α,β) parameter space, beyond the Gaussian case (α=2).
  • Three regimes (1<α<2) show critical transitions and on-off intermittency, with unique critical exponents.
  • Two regimes (0<α≤1) exhibit diverging noise mean, lacking critical transitions and showing always unstable or stable behavior.

Conclusions:

  • Non-equilibrium, power-law noise leads to significantly different statistical and critical behaviors than Gaussian noise.
  • Lévy on-off intermittency offers a new paradigm for understanding complex system dynamics.
  • The identified regimes highlight the rich phenomenology arising from non-Gaussian fluctuations.