Master stability functions reveal diffusion-driven pattern formation in networks

Abstract

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space.For illustration we consider a generalized model of ecological meta-foodwebs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

arXiv comment20 pages, 5 figures, to appear in Phys. Rev. E (2018)

References in corpus (28)

• Catastrophic cascade of failures in interdependent networks
• Synchronization in complex networks
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Mathematical Formulation of Multi-Layer Networks
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• The physics of spreading processes in multilayer networks
• The Multilayer Nature of Ecological Networks
• Random Geometric Graphs
• Centrality in Interconnected Multilayer Networks
• Turing patterns in network-organized activator-inhibitor systems
• Turing patterns on networks
• Explosive synchronization in adaptive and multilayer networks
• The extreme vulnerability of interdependent spatially embedded networks
• Synchronization in networks with multiple interaction layers
• Pattern formation in multiplex networks
• Turing patterns in multiplex networks
• Generalized models as a universal approach to the analysis of nonlinear dynamical systems
• Collapse of an ecological network in Ancient Egypt
• Inter-layer synchronization in multiplex networks
• Several Multiplexes in the same City: The role of wealth differences in urban mobility
• Turing patterns and apparent competition in predator-prey food webs on networks
• Generalized modeling of ecological population dynamics
• Spectral statistics of random geometric graphs
• Impact of dispersal on the stability of metapopulations
• Dynamical analysis of evolution equations in generalized models
• Localization on low-order eigenvectors of data matrices
• Meta-food-chains as a many-layer epidemic process on networks

Cited by in corpus (14)

• Desynchronization transitions in adaptive networks
• Dispersal-induced instability in complex ecosystems
• Multilayer Network Science: from Cells to Societies
• Turing patterns on discrete topologies: from networks to higher-order structures
• Evolutionary game dynamics with environmental feedback in a network with two communities
• Far-ranging generalist top predators enhance the stability of meta-foodwebs
• Sharp thresholds limit the benefit of defector avoidance in cooperation on networks
• Emergence of geometric Turing patterns in complex networks
• Pattern invariance for reaction-diffusion systems on complex networks
• Linguistic evolution driven by network heterogeneity and the Turing mechanism
• Critical parameters of the synchronisation's stability for coupled maps in regular graphs
• Topological conditions drive stability in meta-ecosystems
• Master Stability Functions for metacommunities with two types of habitats
• A stylised view on structural and functional connectivity in dynamical processes in networks