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Noise-induced transitions in random Pomeau-Manneville maps
Tetsu Endo1, Yuzuru Sato2,3, Hiroki Takahasi4
1Department of Physics and Astronomy, Tokyo University of Science, Noda, Chiba 278-8510, Japan.
Chaos (Woodbury, N.Y.)
|September 4, 2025
Summary
Introducing randomness to Pomeau-Manneville maps with dichotomous noise reveals two transitions. Noise-induced changes control orbit convergence and synchronization, offering insights into chaotic systems.
Area of Science:
- Nonlinear Dynamics
- Statistical Physics
- Chaos Theory
Background:
- Pomeau-Manneville (PM) maps model intermittent chaos.
- Understanding noise effects in dynamical systems is crucial.
Purpose of the Study:
- Investigate the impact of dichotomous multiplicative noise on PM maps.
- Characterize noise-induced transitions and resulting dynamical behaviors.
Main Methods:
- Incorporated dichotomous multiplicative noise into PM maps.
- Analyzed the separation of nearby orbits.
- Controlled the probability of repelling map selection.
Main Results:
- Identified two noise-induced transitions based on repelling map probability.
- Observed orbit convergence to an indifferent fixed point for probabilities < 1/2.
- Found weak synchronization and transitions to chaos/weak chaos for probabilities > 1/2.
- Demonstrated a universal power-law exponent of 3/2 at the first transition.
Conclusions:
- Dichotomous noise introduces rich dynamics, including synchronization, in chaotic systems.
- Noise-induced transitions alter the long-term behavior of intermittent systems.
- Results offer insights into noise effects in chaotic and weakly chaotic dynamical systems.
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