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Transient chaos in the Lorenz-type map with periodic forcing
Oleg V Maslennikov1, Vladimir I Nekorkin1, Jürgen Kurths1
1Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia.
Chaos (Woodbury, N.Y.)
|April 2, 2018
Summary
Periodic forcing of chaotic systems reveals non-exponential decay in transient chaos dynamics. The study analyzes how forcing affects escape rates and system behavior, offering insights into complex system perturbations.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Statistical Physics
Background:
- Systems with chaotic attractors can exhibit boundary crises, leading to distinct persistent and transient chaos regimes.
- Understanding transient chaos is crucial for predicting system behavior near critical parameter values.
Purpose of the Study:
- To investigate the effects of periodic forcing on a system undergoing a boundary crisis of a chaotic attractor.
- To analyze how periodic oscillations of the control parameter influence transient chaotic dynamics and escape rates.
Main Methods:
- Perturbation of a system exhibiting a boundary crisis using periodic forcing.
- Analysis of the survival probability function to identify decay behavior.
- Investigation of the impact of forcing frequency and amplitude on the escape rate.
- Examination of phase-space dynamics and the influence of initial conditions.
Main Results:
- Observed non-exponential decay in the survival probability function, deviating from typical transient chaos.
- Quantified the influence of forcing frequency and amplitude on the system's escape rate.
- Characterized the phase-space dynamics under periodic forcing.
- Demonstrated the sensitivity of the system's transient behavior to initial conditions.
Conclusions:
- Periodic forcing significantly alters transient chaotic dynamics, leading to non-exponential decay patterns.
- Forcing parameters (frequency and amplitude) critically influence the escape rate and overall system stability.
- The study highlights the complex interplay between periodic perturbations and chaotic system boundaries.
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