Stationary patterns in star networks of bistable units: Theory and application to chemical reactions

Abstract

We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, uniform state is expected with active or inactive elements at small or large degree networks respectively. Nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).

9 pages, 8 figures

References in corpus (13)

• Synchronization in complex networks
• Turing patterns in network-organized activator-inhibitor systems
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Chimera-like states in modular neural networks
• Pattern formation in multiplex networks
• Turing patterns in multiplex networks
• Robustness of Optimal Synchronization in Real Networks
• Traveling and pinned fronts in bistable reaction-diffusion systems on network
• Propagation failure of excitation waves on trees and random networks
• Effect of small-world topology on wave propagation on networks of excitable elements
• Complex Rotating Waves and Long Transients in a Ring-Network of Electrochemical Oscillators with Sparse Random Cross-Connections
• Self-Organized Stationary Patterns in Networks of Bistable Chemical Reactions
• Feedback-induced stationary localized patterns in networks of diffusively coupled bistable elements

Cited by in corpus (4)

• Networks beyond pairwise interactions: structure and dynamics
• Intertangled stochastic motifs in networks of excitatory-inhibitory units
• Localized patterns in star networks of Class B lasers with optoelectronic feedback
• Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements