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Persistence of chaos in a time-delayed-feedback controlled Duffing system
Kohei Yamasue1, Takashi Hikihara
1Department of Electrical Engineering, Kyoto University, Katsura, Nishikyo, Kyoto 615-8510, Japan.
Summary
This study shows time-delayed feedback control preserves chaotic dynamics in a two-well Duffing system. This leads to complex behavior and extended chaotic transients before reaching stable states.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Control systems
Background:
- The Duffing oscillator is a classic model for nonlinear dynamics.
- Time-delayed feedback control is used to influence system behavior.
- Understanding global phase structures is crucial for predicting system dynamics.
Purpose of the Study:
- To investigate the global phase structures of a time-delayed-feedback controlled two-well Duffing system.
- To determine how chaotic dynamics are affected by the control strategy.
- To analyze the implications of these structures on system behavior and convergence.
Main Methods:
- Analysis of global phase structures.
- Investigation of unstable manifolds and fixed points in function space.
- Characterization of chaotic dynamics inheritance.
Main Results:
- The controlled system inherits the global chaotic dynamics from the original system.
- A global stretch and fold structure persists along an unstable manifold.
- The inherited chaotic dynamics result in a complex domain of attraction and long chaotic transients.
Conclusions:
- Time-delayed feedback control does not eliminate chaos in the two-well Duffing system.
- The system exhibits persistent chaotic behavior and complex attractors.
- Predicting long-term system convergence requires accounting for these chaotic transients.
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