Chimera states for directed networks

Area of Science:

• Complex systems
• Nonlinear dynamics
• Network science

Background:

• Chimera states, a unique phenomenon where coherence and incoherence coexist in identical elements, have been observed in various oscillatory systems.
• Understanding the emergence and dynamics of chimera states in coupled oscillator networks is crucial for fields ranging from neuroscience to power grids.

Purpose of the Study:

• To investigate the formation and evolution of chimera states in ensembles of phase oscillators with unidirectional coupling.
• To explore the influence of network size and coupling range on chimera behavior.

Main Methods:

• Simulations of phase oscillator ensembles with varying numbers of elements (three and one hundred).
• Analysis of parameter space to identify regions exhibiting chimera states.
• Investigation of the role of unidirectional coupling and its range in the emergence of chimeras.

Main Results:

• Tiny chimera islands were observed in small networks (cyclic triple), surrounded by chaotic switching due to counter-propagating waves.
• In larger networks (cyclic century), these islands merged into a single 'chimera continent' encompassing diverse chimera configurations.
• The phenomenon is prominent in networks with intermediate unidirectional coupling ranges and diminishes with decreasing range.

Conclusions:

• Unidirectional coupling in phase oscillator networks can robustly generate chimera states.
• Network size plays a significant role in the global manifestation of chimera behavior, transitioning from islands to a continent.
• The range of unidirectional coupling is a critical parameter determining the presence and extent of chimera phenomena.