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Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities.
Adrian-Mihail Stoica1, Isaac Yaesh2
1Faculty of Aerospace Engineering, University Politehnica of Bucharest, 060042 Bucharest, Romania.
Entropy (Basel, Switzerland)
|February 23, 2024
Summary
Stochastic antiresonance can stabilize unstable nonlinear systems using state-multiplicative noise. This method, applicable in engineering and biology, leverages noise to control chaotic behavior.
Area of Science:
- Nonlinear Dynamics and Control Systems
- Stochastic Systems Analysis
- Applied Mathematics
Background:
- Nonlinear systems with sector-bounded nonlinearities are prevalent in engineering, physics, and biology.
- These systems can exhibit unstable or chaotic behavior in the absence of noise.
- Approximations using neural networks, like Hopfield networks, also present similar dynamic challenges.
Purpose of the Study:
- To investigate the application of stochastic antiresonance for stabilizing nonlinear systems.
- To demonstrate that state-multiplicative noise can be used to stabilize systems that are unstable without noise.
- To develop theoretical conditions for noise-induced stabilization.
Main Methods:
- Consideration of stochastic antiresonance for nonlinear systems with sector-bounded nonlinearities.
- Derivation of stabilization conditions using Linear-Matrix-Inequality (LMI) techniques.
- Utilization of a novel non-quadratic Lyapunov functional for stability analysis.
Main Results:
- It is shown that specific levels of state-multiplicative noise can stabilize otherwise unstable nonlinear systems.
- Linear-Matrix-Inequality-based conditions for stabilization are derived.
- A numerical example demonstrates the stabilization of a chaotic nonlinear system using state-multiplicative noise.
Conclusions:
- State-multiplicative noise offers a viable mechanism for stabilizing unstable nonlinear systems.
- The developed LMI-based conditions provide a rigorous framework for designing noise-induced stabilization strategies.
- Stochastic antiresonance is a powerful paradigm for controlling complex nonlinear dynamics.
Keywords:
infinitesimal generatorsector-bounded nonlinearitiesstability analysisstochastic antiresonancestochastic systems with state- dependent noiseMore Related Videos
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