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Chimera states in purely local delay-coupled oscillators
Bidesh K Bera1, Dibakar Ghosh1
1Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India.
Physical Review. E
|June 15, 2016
Summary
This study explores chimera states in coupled chaotic and limit-cycle oscillators. Time delays in nonlinear local coupling can eliminate chimera states by shrinking coherent regions.
Area of Science:
- Nonlinear dynamics
- Complex systems
- Network science
Background:
- Chimera states, a unique synchronization pattern, occur in networks of coupled oscillators.
- Understanding chimera states is crucial for various fields, including neuroscience and physics.
- Local coupling in oscillator networks presents unique challenges for chimera state formation.
Purpose of the Study:
- To investigate the existence and conditions for chimera states in networks of locally coupled chaotic and limit-cycle oscillators.
- To analyze the impact of time delay and nonlinear coupling on chimera and multichimera states.
- To identify the key role of nonlinearity in the coupling function for chimera state emergence.
Main Methods:
- Numerical simulations of coupled Hindmarsh-Rose neuron models.
- Analysis of time-delayed Mackey-Glass systems and Van der Pol oscillators.
- Investigation of parameter spaces, including synaptic coupling strength and time delay.
Main Results:
- Chimera and multichimera states were numerically observed in locally coupled Hindmarsh-Rose neurons.
- Time delay in nonlinear local coupling was found to reduce the coherent region, potentially eliminating chimera states.
- Chimera states were also observed in time-delayed Mackey-Glass and Van der Pol systems, highlighting the role of nonlinearity.
Conclusions:
- Nonlinearity in the coupling function is essential for the emergence of chimera or multichimera states.
- Time delay in local coupling significantly influences the existence and stability of chimera states.
- A phase diagram for chimera states was identified across a broad parameter space.
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