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Dynamical Multimodality in Systems Driven by Ornstein-Uhlenbeck Noise.

Michał Mandrysz¹, Bartłomiej Dybiec²

¹Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland.

Entropy (Basel, Switzerland)

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Summary

This summary is machine-generated.

Correlated noise, like Ornstein-Uhlenbeck noise, can create multiple stable states in dynamical systems. Combining it with dichotomous noise further controls these multimodalities.

Keywords:

Ornstein–Uhlenbeck process dichotomous noise stationary density stochastic dynamics

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Area of Science:

Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

Dynamical systems are influenced by deterministic forces and random fluctuations (noise).
Non-white (correlated) noise can lead to stationary states with more modes than the deterministic potential's stable fixed points.
Ornstein-Uhlenbeck noise specifically can induce bimodality in single-well potentials.

Purpose of the Study:

Investigate the emergence of dynamical multimodality.
Explore systems with simultaneous Ornstein-Uhlenbeck and Markovian dichotomous noise.
Analyze 1D and 2D setups.

Main Methods:

Simultaneous application of Ornstein-Uhlenbeck and dichotomous noise.
Analysis of 1D and 2D dynamical systems.
Examination of stationary state properties.

Main Results:

The combined action of Ornstein-Uhlenbeck and dichotomous noise can induce multimodality.
Dichotomous noise randomizes the potential, enabling control over the number of modes.
Dynamical multimodality is achievable in both 1D and 2D systems.

Conclusions:

The interplay of different noise types offers a mechanism for controlling system complexity.
Potential randomization by dichotomous noise is key to managing stationary state modes.
This research provides insights into noise-induced phenomena in complex systems.