Self-organized patterns on complex networks  (SPCN) Session 1

Abstract: Multistability?understood as the existence of diverse stationary states under a fixed set of conditions?is ubiquitous in physics and in biology, it and leads to interesting spatial and temporal patterns. Motivated by several empirical observation of bimodal distributions of activity, we propose and analyze a theory for the self-organization to the point of phase-coexistence in systems exhibiting a first-order phase transition. It explains the emergence of regular avalanches patterns with attributes of scale-invariance which coexist with huge anomalous ones, with realizations in many fields. Close

Abstract: Since Turing?s seminal work, reaction-diffusion models have played a central role in the analysis of various self-organized spatio-temporal patterns in nature. As pointed out by Othmer and Scriven already in 1971, it is straightforward to generalize the reaction-diffusion models to networks, which gives us a wider perspective on pattern formation. In this talk, several topics on pattern formation and collective dynamics in reaction-diffusion models on random networks will be discussed. We consider formation of Turing patterns in activator-inhibitor systems on networks, where difference in diffusivity of chemical species leads to destabilization of uniform states and formation of patterns. It is shown that, for networks with degree heterogeneity, simple mean-field approximation of the network can account for backbones of the developed patterns. We will also see that essentially the same mechanism, called Benjamin-Feir instability, destabilizes uniformly synchronized state and leads to collective dynamics in coupled oscillators on networks. More general types of diffusion-induced instabilities in reaction-diffusion systems with three chemical species or in directed networks will also be discussed. Some related unsolved issues, such as self-consistency analysis of developed patterns, bifurcation analysis of instability, and localization properties of Laplacian eigenmodes on networks, will also be mentioned. Close

Abstract: Pattern formation has attracted the interest of the scientific communities of several fields since the Turing seminal paper on morphogenesis [1] first appeared. Recently, patterns emergence has been studied in complex networks [2], where a spontaneous differentiation of nodes in activator(inhibitor)-rich and activator(inhibitor)-poor nodes was observed in a two species reaction-diffusion system. From then, several extensions and generalizations have followed. In this talk we aim reviewing the main framework of our research on the pattern formation theory from the network prospective. Starting from the Turing instability mechanism we prove that the spontaneous segregation of the nodes in different groups extends far beyond Turing original conditions. In particular the network topology plays an active role in the initialization of the self-organization process as it happens for the directed networks [3]. In other cases the peculiarities of the network structure in layers (multiplex [4]) or product of sub-networks (Cartesian network [5]) explain why motifs are more likely to appear in such networks than others or how they emerge as a collective property of networks. Different applications from ecology to neuroscience can rise. Close

Abstract: TBA Close