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Scaling laws for noise-induced super-persistent chaotic transients
1Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, USA.
Summary
Noise can create super-persistent chaotic transients, extending their lifetime dramatically via double-exponential scaling. However, in some cases, noise can shorten these long-lived chaotic transients.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Statistical Physics
Background:
- Super-persistent chaotic transients exhibit extremely long lifetimes governed by specific scaling laws.
- The relevance of these transients to turbulence has been a long-standing question.
- Understanding the influence of noise on chaotic dynamics is crucial.
Purpose of the Study:
- To investigate noise-induced super-persistent chaotic transients.
- To construct a model illustrating this phenomenon.
- To derive scaling laws for transient lifetimes under varying noise conditions.
Main Methods:
- Construction of a prototype model using random maps.
- Approximation of the model using stochastic differential equations.
- Derivation of scaling laws for transient lifetime versus noise amplitude.
Main Results:
- In the subcritical case (without noise), noise induces super-persistent transients with double-exponential and algebraic scaling.
- Noise significantly reduces transient lifetimes in the supercritical case.
- The study reveals complex interplay between random and deterministic chaotic dynamics.
Conclusions:
- Noise can dramatically enhance transient persistence in chaotic systems.
- The impact of noise on transient lifetimes is dependent on the system's parameters (subcritical vs. supercritical).
- These findings have significant implications for understanding turbulence and complex systems.