Coexisting synchronous and asynchronous states in locally coupled array of oscillators by partial self-feedback...

Area of Science:

• Nonlinear dynamics
• Complex systems
• Theoretical physics

Background:

• Oscillator arrays exhibit complex behaviors, including synchronization and desynchronization.
• Chimera states represent a unique phenomenon where coherent and incoherent subpopulations coexist within an array.

Purpose of the Study:

• To investigate the emergence of coexisting synchronous and asynchronous subpopulations in one-dimensional oscillator arrays.
• To explore the effect of self-feedback control on the dynamics of these arrays.
• To understand the tunability of coherent and incoherent states.

Main Methods:

• Applying self-feedback control to subpopulations of identical oscillators in one-dimensional arrays.
• Utilizing numerical simulations.
• Employing the Landau-Stuart system and the Kuramoto-Sakaguchi phase model.

Main Results:

• Self-feedback control induced the emergence of coexisting synchronous and asynchronous subpopulations.
• The system exhibited behavior analogous to chimera states, with subpopulations splitting into coherent and incoherent states.
• The sizes of coherent and incoherent subpopulations could be controlled by adjusting nearest-neighbor coupling and self-feedback strength, though precise control was unpredictable.

Conclusions:

• Self-feedback is an effective mechanism for generating complex dynamic states in oscillator arrays.
• The study demonstrates a method for controlling the balance between order and disorder in coupled oscillator systems.
• The findings contribute to the understanding of emergent phenomena in complex systems and nonlinear dynamics.