ABSTRACT
Networks of coupled cells are schematically identified with directed graphs, where the nodes represent dynamical systems, and the arrows indicate the couplings between them. This chapter analyzes a fractional-order model of a network of one ring of three cells coupled to a “buffer” cell. Possible explanations for the peculiar patterns are the symmetry of the network, the dynamical characteristics of the Chen oscillator, used to model the cells’ internal dynamics, and the order of the fractional derivative. The chapter reviews some concepts of fractional calculus, and highlights important notions of the theory of coupled cell networks, for symmetric dynamical systems. A network of cells is represented as a directed graph, where the nodes represent the cells and the arrows the couplings between them. Cells of the same type have the same internal dynamics, and arrows with the same label identify equal couplings. The chapter considers an important class of networks, namely, the ones that possess a group of symmetries.
