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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Gradient systems on coupled cell networks

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Author(s):
Manoel, Miriam [1] ; Roberts, Mark [2, 3]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, ICMC, Dept Math, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey - England
[3] African Inst Math Sci, Arusha - Tanzania
Total Affiliations: 3
Document type: Journal article
Source: Nonlinearity; v. 28, n. 10, p. 3487-3509, OCT 2015.
Web of Science Citations: 2
Abstract

For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell graph, and we use tools from graph theory to deduce the general form of such functions, relating it to the topological structure of the graph defining the network. The coupling of pairs of dynamical systems cells is represented by edges of the graph, and from spectral graph theory we detect the existence and nature of equilibria of the gradient system from the critical points of the coupling function. In particular, we study fully synchronous and 2-state patterns of equilibria on regular graphs. These are two special types of equilibrium configurations for gradient networks. We also investigate equilibrium configurations of S-1-invariant admissible functions on a ring of cells. (AU)

FAPESP's process: 13/11108-7 - Symmetries of functions on networks and of mappings on Minkowski spaces
Grantee:Míriam Garcia Manoel
Support type: Scholarships abroad - Research