Controlling chimera states via minimal coupling modification

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Chimera states are complex emergent phenomena observed in networks of coupled oscillators, characterized by coexisting synchronized and desynchronized behavior.
• Controlling chimera states is crucial for understanding and potentially harnessing complex network dynamics.

Purpose of the Study:

• To propose and investigate a method for controlling chimera states in nonlocally coupled phase oscillator networks.
• To identify the minimal modifications to network connectivity required for chimera state control.

Main Methods:

• The study focuses exclusively on manipulating network connectivity to control chimera states.
• A 'pacemaker' oscillator, with unidirectional links, is introduced as a mechanism to influence chimera formation and location.
• The impact of minimal connectivity changes, such as altering a single connection's strength, is explored.

Main Results:

• A pacemaker oscillator can induce chimera states under conditions where they would not spontaneously form.
• The pacemaker effectively attracts the incoherent population of the chimera state, allowing for positional control.
• Less invasive modifications, like adjusting the strength of a single connection, are sufficient to achieve chimera control.

Conclusions:

• Network connectivity is a powerful tool for controlling complex emergent phenomena like chimera states.
• Minimal, targeted modifications to network structure can significantly influence and control collective oscillator behavior.
• The findings offer insights into the fundamental mechanisms governing synchronization and pattern formation in complex networks.