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Noise-induced transitions in state-dependent dichotomous processes.
Francesco Laio1, Luca Ridolfi, Paolo D'Odorico
1Dipartimento di Idraulica, Trasporti ed Infrastrutture Civili, Politecnico di Torino, Torino, Italy. francesco.laio@polito.it
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
Feedback between dynamical systems and dichotomous Markov noise can alter system stability. Positive feedback may induce bistability, while noise can either induce or destroy bistability depending on feedback strength.
Area of Science:
- Physics
- Applied Mathematics
- Nonlinear Dynamics
Background:
- Stochastic systems often use dichotomous Markov noise, typically assumed independent of system dynamics.
- Real-world systems can exhibit feedback between the noise and the system's state.
- Investigating this feedback is crucial for understanding complex stochastic behavior.
Purpose of the Study:
- To analyze stochastic systems with state-dependent dichotomous Markov noise.
- To explore how feedback influences noise-induced transitions and system stability.
- To clarify the relationship between stochastic dynamics and their deterministic counterparts.
Main Methods:
- Modeling systems with dichotomous Markov noise where transition rates depend on the system's state.
- Analyzing the impact of positive and negative feedback on system dynamics.
- Investigating noise-induced transitions and the emergence/destruction of bistability.
Main Results:
- Negative feedback maintains monostability in systems with a single stable point.
- Positive feedback can induce bistability in the deterministic dynamics.
- Noise can induce bistability even with null or negative feedback.
- Noise can also destabilize positive feedback-induced bistability, leading to a single intermediate stable state.
Conclusions:
- Feedback significantly alters the stability landscape of stochastic systems.
- The interplay between feedback and noise can lead to complex phenomena like induced or suppressed bistability.
- Careful consideration of feedback mechanisms is essential for accurate modeling of stochastic systems.
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