Synchronization of Heterogeneous Oscillators by Noninvasive Time-Delayed Cross Coupling

Area of Science:

• Physics
• Nonlinear Dynamics
• Control Theory

Background:

• Synchronization is a fundamental phenomenon in coupled dynamical systems.
• Achieving synchronization in nonidentical systems, especially those with different time scales, presents significant challenges.
• Existing methods often require identical systems or specific coupling configurations.

Purpose of the Study:

• To demonstrate that nonidentical nonlinear oscillators can achieve synchronization.
• To introduce a novel synchronization strategy using mutual coupling via time-delayed control signals.
• To investigate the behavior of synchronized oscillators settling on unstable states.

Main Methods:

• Theoretical analysis of coupled nonlinear oscillators with time-delayed feedback.
• Numerical simulations to verify synchronization and analyze system dynamics.
• Experimental validation using nonlinear electronic oscillators.

Main Results:

• Nonidentical nonlinear oscillators with different time scales were successfully synchronized.
• The synchronized oscillators settled onto unstable states, such as fixed points or unstable periodic orbits.
• The coupling force was shown to vanish in the long time limit.

Conclusions:

• Time-delayed mutual coupling is an effective method for synchronizing nonidentical nonlinear oscillators.
• The synchronization mechanism leads to stable convergence to unstable states.
• The experimental demonstration confirms the theoretical predictions and numerical findings.