Automatic control and tracking of periodic orbits in chaotic systems

Area of Science:

• Nonlinear dynamics
• Chaos theory
• Control theory

Background:

• Chaotic systems exhibit complex, unpredictable behavior.
• Controlling chaotic dynamics is crucial for various scientific and engineering applications.
• Existing methods for controlling unstable periodic orbits often require detailed system knowledge or reference states.

Purpose of the Study:

• To develop a novel strategy for controlling periodic orbits in chaotic dynamics.
• To track and stabilize unstable periodic orbits embedded within a chaotic attractor.
• To overcome limitations of existing control techniques for chaotic systems.

Main Methods:

• Automatic feedback adjustment of an additional parameter in a dynamical system.
• Application to both discrete- and continuous-time systems.
• Assessment of effectiveness and robustness through stabilization of unstable periodic orbits.

Main Results:

• Successfully demonstrated a method for controlling periodic orbits in chaotic dynamics.
• The proposed strategy enables tracking toward unstable periodic orbits.
• The technique proved effective and robust in stabilizing these orbits across different system types.

Conclusions:

• The developed method offers a robust and information-independent approach to controlling chaotic dynamics.
• It provides a valuable tool for stabilizing unstable periodic orbits.
• This technique advances the field of chaos control by simplifying requirements and enhancing applicability.