Chimera Patterns in Networks: Interplay Between Dynamics, Structure, Noise, and Delay

Preface
Acknowledgements
Contents
1 Chimera Patterns in Complex Networks
	1.1 Introduction
	1.2 Historical Note
	1.3 Definition and Main Features
	1.4 Quantitative Measures
	1.5 Chimera States in Different Systems
	1.6 Chimera States in Networks with Various Topologies
	1.7 Types of Chimera States
	1.8 Control of Chimera States
	1.9 Chimera States in Experiments
	1.10 Applications of Chimera States
2 Amplitude Chimeras and Chimera Death in Ring Networks
	2.1 Introduction
	2.2 Stuart-Landau Model
	2.3 Deterministic Dynamics Without Delay
		2.3.1 Amplitude Chimeras and Chimera Death
		2.3.2 Transient Behavior of Amplitude Chimeras
		2.3.3 Detection of Transient Time of Amplitude Chimeras
		2.3.4 Role of Initial Conditions
		2.3.5 Relative Size of the Incoherent Domains
		2.3.6 Impact of System Size
		2.3.7 Stability Analysis of Amplitude Chimeras
		2.3.8 Summary
	2.4 The Role of Time Delay
		2.4.1 Time-Delay Model
		2.4.2 Characterizing the Transition from Incoherence to Coherence
		2.4.3 The Impact of Various Time Delay Types
		2.4.4 Summary
	2.5 The Role of Noise
		2.5.1 Stochastic Model
		2.5.2 Deterministic Chimera Patterns
		2.5.3 Influence of Noise on Transient Times
		2.5.4 Maps of Dynamic Regimes
		2.5.5 Summary
	2.6 Conclusions
3 Coherence-Resonance Chimeras in Ring Networks
	3.1 Introduction
	3.2 FitzHugh-Nagumo Model
	3.3 Coherence-Resonance Chimeras Without Time Delays
		3.3.1 Coherence Resonance in a Single FitzHugh-Nagumo System
		3.3.2 Chimera States in Oscillatory and Excitable Regimes
		3.3.3 Alternating Behavior of Coherence-Resonance Chimeras
		3.3.4 Network Dynamics in the Presence of Strong Noise
		3.3.5 Dynamic Regimes: The Impact of Coupling Parameters
		3.3.6 Characterization of Coherence-Resonance Chimera
		3.3.7 Summary
	3.4 Time-Delayed Feedback Control of Chimera States
		3.4.1 Coherence-Resonance Chimeras in the Presence of Time-Delayed Feedback
		3.4.2 Dynamic Regimes in the Presence of Time-Delayed Feedback
		3.4.3 Impact of the Feedback on Coherence-Resonance Chimera Existence: Noise Intensity Range
		3.4.4 Impact of the Feedback on Coherence-Resonance Chimera Existence: Threshold Parameter Range
		3.4.5 Summary
	3.5 Conclusions
4 Towards Realistic Topologies: Coherence, Incoherence, and Partial Synchronization Patterns
	4.1 Introduction
	4.2 Coherence Resonance in Multiplex Networks
		4.2.1 Model
		4.2.2 Dynamics of Isolated Layers
		4.2.3 Multiplex Network: Intra-layer Coupling Strength Mismatch
		4.2.4 A Deterministic Layer Multiplexed with a Noisy Layer
		4.2.5 Summary
	4.3 Coherence-Incoherence Patterns in Multiplex Networks
		4.3.1 Model
		4.3.2 Dynamics of Isolated Layers
		4.3.3 Multiplex Network: Coupling Range Mismatch
		4.3.4 Multiplex Network: Coupling Strength Mismatch
		4.3.5 Multiplex Network: Switching to Solitary States
		4.3.6 Summary
	4.4 Coherence-Incoherence Patterns in Networks with Power-Law Coupling
		4.4.1 Model
		4.4.2 Dynamic Regimes: Impact of Coupling Parameters
		4.4.3 Chimera States
		4.4.4 Tree-Like Patterns
		4.4.5 Solitary States
		4.4.6 Transition Patterns
		4.4.7 Summary
	4.5 Coherence-Incoherence Patterns in Networks with Fractal Connectivities
		4.5.1 Ring Networks of Van der Pol Oscillators
		4.5.2 Ring Networks of FitzHugh-Nagumo Oscillators with Time Delay
		4.5.3 2D Modular Fractal Connectivities in Networks of FitzHugh-Nagumo Oscillators
	4.6 Conclusions
References
Index