Synchronization of non-identical systems by non-invasive mutual time-delayed feedback

Area of Science:

• Complex Systems
• Control Theory
• Information Security

Background:

• Synchronization of coupled dynamical systems is a fundamental phenomenon with applications in various fields.
• Achieving synchronization between non-identical systems presents significant theoretical and practical challenges.
• Time-delayed feedback control offers a promising avenue for manipulating system dynamics.

Purpose of the Study:

• To investigate the synchronization of non-identical systems using mutual time-delayed feedback.
• To develop an analytic method for understanding the synchronization process and its limitations.
• To explore the application of this synchronization technique in secure communication.

Main Methods:

• Employing time-delayed feedback control principles.
• Utilizing an asymptotically vanishing interaction strength.
• Developing an analytic perturbation scheme to analyze the system's behavior.

Main Results:

• Demonstrated successful synchronization of non-identical systems via mutual time-delayed feedback.
• The analytic perturbation scheme revealed the advantages and limitations of the proposed control method.
• Identified the feasibility of using this approach for secure communication.

Conclusions:

• Mutual time-delayed feedback with vanishing interaction is an effective strategy for synchronizing non-identical systems.
• The developed analytic framework provides valuable insights into the control mechanism.
• The findings open new possibilities for secure communication systems based on synchronization dynamics.