Towards Realistic Topologies: Coherence, Incoherence, and Partial Synchronization Patterns

Abstract

In the present chapter, we investigate network topologies beyond nonlocally coupled rings. In particular, we focus on multilayer networks, networks with power-law coupling kernel, and networks with fractal connectivities. First, we consider coherence resonance in multiplex networks. Then, we explore chimera states and solitary states in multiplex networks. Further, we study coherence-incoherence patterns in networks with power-law coupling kernel. Finally, we discuss the formation of chimera patterns in two types of networks with fractal connectivities: ring networks with fractal connectivities and networks with 2D modular fractal connections. We use FitzHugh-Nagumo model and Van der Pol oscillator to describe the individual node dynamics.