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Controlled transitions between cupolets of chaotic systems
Matthew A Morena1, Kevin M Short1, Erica E Cooke1
1Integrated Applied Mathematics Program, University of New Hampshire, Durham, New Hampshire 03824, USA.
Chaos (Woodbury, N.Y.)
|April 5, 2014
Summary
This study introduces a method to stabilize chaotic systems using unique control sequences for specific orbits called cupolets. Dijkstra's algorithm minimizes chaotic transients during transitions between these orbits.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Control Theory
Background:
- Chaotic systems possess unstable periodic orbits (UPOs) that form a skeleton of the system's dynamics.
- Controlling these UPOs is crucial for understanding and manipulating chaotic behavior.
- Existing methods may lead to significant chaotic transients during state transitions.
Purpose of the Study:
- To present an efficient control scheme for stabilizing UPOs in chaotic systems, termed cupolets.
- To demonstrate a method for unique identification and transition between cupolets using control sequences.
- To minimize chaotic transients during cupolet transitions and ensure control certainty.
Main Methods:
- Stabilization of UPOs by developing a control scheme.
- Unique identification of cupolets via specific control sequences.
- Application of Dijkstra's shortest path algorithm for minimizing transients and steering chaotic systems.
Main Results:
- Successfully stabilized UPOs, creating identifiable cupolets.
- Demonstrated unique mapping between control sequences and cupolets.
- Minimized chaotic transients during transitions using Dijkstra's algorithm, enhancing control certainty.
Conclusions:
- The proposed control scheme offers an efficient way to stabilize and navigate chaotic systems.
- Dijkstra's algorithm provides an effective tool for steering chaotic systems with minimal transients.
- This approach enhances predictability and control in nonlinear dynamical systems.
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