Stochastic Turing Patterns on a Network

Abstract

The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically, and eventually traced back to the finite size corrections stemming from the inherent graininess of the scrutinized medium.

The movies referred to in the paper are provided upon request. Please send your requests to Duccio Fanelli ([email protected]) or Francesca Di Patti ([email protected])

References in corpus (3)

• Turing patterns in network-organized activator-inhibitor systems
• Quasi-cycles in a spatial predator-prey model
• Stochastic waves in a Brusselator model with nonlocal interaction

Cited by in corpus (23)

• Turing patterns mediated by network topology in homogeneous active systems
• Does the brain behave like a (complex) network? I. Dynamics
• The linear noise approximation for reaction-diffusion systems on networks
• Turing instability in Reaction-Diffusion models on complex networks
• Tune the topology to create or destroy patterns
• Turing patterns on discrete topologies: from networks to higher-order structures
• Multiple scale theory of topology driven pattern on directed networks
• Benjamin-Feir instabilities on directed networks
• Global topological control for synchronized dynamics on networks
• Turing instability in quantum activator-inhibitor systems
• Binary-state dynamics on complex networks: Stochastic pair approximation and beyond
• Resilience for stochastic systems interacting via a quasi-degenerate network
• Desynchronization and pattern formation in a noisy feedforward oscillators network
• Pattern formation for reactive species undergoing anisotropic diffusion
• Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions
• Graph spectral characterisation of the XY model on complex networks
• Unilateral regulation breaks regularity of Turing patterns
• Intertangled stochastic motifs in networks of excitatory-inhibitory units
• Amplitude death and restoration in networks of oscillators with random-walk diffusion
• Drift-induced Benjamin-Feir instabilities
• Spectral control for ecological stability
• Turing instability in a model with two interacting Ising lines: linear stability and non-equilibrium fluctuations
• Modeling of Sensory Characteristics Based on the Growth of Food Spoilage Bacteria