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Maintenance of transient chaos using a neural-network-assisted feedback control
J F Louvier-Hernández1, R Rico-Martínez, P Parmananda
1Departamento de Ingeniería Química, Instituto Tecnológico de Celaya, Avenida. Tecnológico y A. García Cubas s/n, 38010, Celaya, Guanajuato, Mexico.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
Summary
Researchers destabilized a stable period-3 orbit to maintain chaotic transients using two feedback strategies. These methods exclude trajectories near the attractor, employing artificial neural networks for control.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Control Theory
Background:
- Stable periodic orbits can exist near chaotic attractors.
- Chaotic transients are short-lived, unpredictable trajectories.
- Controlling chaotic systems is a significant challenge.
Purpose of the Study:
- To destabilize a stable period-3 orbit.
- To induce and sustain chaotic transients.
- To explore novel feedback control strategies for chaos management.
Main Methods:
- Utilized two distinct feedback strategies to destabilize a period-3 orbit.
- Employed trajectory exclusion from the vicinity of the stable orbit.
- Implemented artificial neural networks as reference models for control.
Main Results:
- Successfully destabilized the period-3 orbit, leading to chaotic behavior.
- Achieved maintenance of otherwise short-lived chaotic transients.
- Demonstrated the efficacy of both proportional feedback and predictive feedback methods.
Conclusions:
- Feedback control can be used to manipulate the dynamics of chaotic systems.
- Artificial neural networks are effective tools for implementing complex control strategies.
- The presented methods offer a pathway to control and prolong chaotic transient behavior.