Abstract
Dynamical processes in many engineered and living systems take place on complex networks of discrete dynamical units. We present laboratory experiments with a networked chemical system of nickel electrodissolution in which synchronization patterns are recorded in systems with smooth periodic, relaxation periodic, and chaotic oscillators organized in networks composed of up to twenty dynamical units and 140 connections. The reaction system formed domains of synchronization patterns that are strongly affected by the architecture of the network. Spatially organized partial synchronization could be observed either due to densely connected network nodes or through the ‘chimera’ symmetry breaking mechanism. Relaxation periodic and chaotic oscillators formed structures by dynamical differentiation. We have identified effects of network structure on pattern selection (through permutation symmetry and coupling directness) and on formation of hierarchical and ‘fuzzy’ clusters. With chaotic oscillators we provide experimental evidence that critical coupling strengths at which transition to identical synchronization occurs can be interpreted by experiments with a pair of oscillators and analysis of the eigenvalues of the Laplacian connectivity matrix. The experiments thus provide an insight into the extent of the impact of the architecture of a network on self-organized synchronization patterns.
Highlights
Inspired by many chemical [1,2] and biological [3] examples, self-organized spatiotemporal structures have been often studied [4] In reaction-diffusion type systems where system interaction is localized by diffusion, or in globally coupled systems where the interaction is assumed to be dense enough to be considered global
Because of the presence of these prevalent network structures, intense research was focused on the existence of prototype dynamical phenomena on networks and on novel collective behaviors that are induced by the network structure and cannot be seen with local or global interactions [11]
A fundamental question is the relationship between the observed synchronization pattern and the architectural and statistical features of the underlying network structure for various types of synchrony for different types of oscillators of varying inherent heterogeneities [10,16]
Summary
Inspired by many chemical [1,2] and biological [3] examples, self-organized spatiotemporal structures have been often studied [4] In reaction-diffusion type systems where system interaction is localized by diffusion, or in globally coupled systems where the interaction is assumed to be dense enough to be considered global (or there exists a physical global constraint). Synchronization patterns on networks [10] have relevance in a wide range of fields where the discrete units exhibit oscillatory behavior; examples include biological clocks [12], neuronal networks in the mammalian forebrain [13], epileptic seizure dynamics [14], or power grids [15]. A fundamental question is the relationship between the observed synchronization pattern and the architectural and statistical features of the underlying network structure for various types of synchrony (phase, generalized, or identical synchronization, clustering, phase waves) for different types of oscillators (smooth vs relaxation vs chaotic oscillators) of varying inherent heterogeneities [10,16]. Nonlocal coupling of identical phase oscillators with a phase lag in their interaction functions can induce a non-trivial hybrid ‘chimera’ state where regions of coherent and incoherent states co-exist while in similar configuration a pair or a globally coupled population exhibits perfect synchrony [11,17,18,19,20]
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