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Transitions across a barrier induced by deterministic forcings.
1Institut Royal Météorologique de Belgique, Avenue Circulaire 3, 1180 Brussels, Belgium.
Summary
This study explores how bistable dynamical systems transition between states under deterministic forcing, revealing unique thresholds and behaviors distinct from noise-driven systems. Findings offer insights into system dynamics and probability distributions.
Area of Science:
- Nonlinear Dynamics
- Statistical Physics
- Complex Systems
Background:
- Bistable dynamical systems exhibit two stable states, crucial in various scientific fields.
- Understanding state transitions is key to predicting system behavior.
- Classical Kramers' theory describes noise-induced transitions, but deterministic forcing presents different dynamics.
Purpose of the Study:
- To investigate the kinetics of barrier crossing in bistable systems under deterministic forcing.
- To compare deterministic forcing effects with classical Kramers' theory for noise-induced transitions.
- To analyze thresholds, transition characteristics, and probabilistic properties of the system's response.
Main Methods:
- Analytical derivations of transition kinetics.
- Numerical simulations to complement analytical results.
- Comparison with established theories like Kramers' theory.
Main Results:
- Established the existence of nontrivial thresholds for state transitions under deterministic forcing.
- Derived analytic and numerical results for transition characteristics under periodic and chaotic forcings.
- Identified connections between system response properties and universal stable distributions.
Conclusions:
- Deterministic forcing leads to distinct transition dynamics and thresholds compared to noise-induced transitions.
- The study provides a comprehensive analysis of bistable system responses to various deterministic inputs.
- Findings contribute to understanding complex system dynamics and their probabilistic behavior.