Stylized models of dynamical processes on graphs allow us to explore the relationships between network architecture and dynamics, a topic relevance in range disciplines. One strategy is translate observations into pairwise nodes, often called functional connectivity (FC), quantitatively compare them with or structural (SC). Here, we start from observation that for coupled logistic maps, SC/FC v...

The networks of globally coupled maps with a pacemaker have been introduced. We consider a generalization of the Kaneko model with a pacemaker represented by a single period-doubling element coupled unidirectionally with a set of other mutually coupled cells. We also investigate the dynamics of a system of two unidirectionally coupled elements, which manifests a special type of critical behavio...

Bhaskar and Lakshimkantham proved the existence of coupled fixed point for a single valued mapping under weak contractive conditions and as an application they proved the existence of a unique solution of a boundary value problem associated with a first order ordinary differential equation. Recently, Lakshmikantham and Ćirić obtained a coupled coincidence and coupled common fixed point of two s...

We study the critical behavior (CB) of all period p-tuplings (p=2, 3, 4, . . .) in N (N =2, 3, 4, . . .) symmetrically coupled one-dimensional maps. We first investigate the CB for the N = 2 case of two coupled maps, using a renormalization method. Three (five) kinds of fixed points of the renormalization transformation and their relevant “coupling eigenvalues” associated with coupling perturba...