Periodic-orbit (PO) formulas for chaotic-diffusion probability distributions (PDs) are examined in the case of the perturbed Arnol'd cat map on the cylinder. This translationally invariant system exhibits a transition from uniform to nonuniform hyperbolicity as the perturbation parameter is...

In this study, the dynamics of decisions in complex networks subject to external fields are studied within a Markov process framework using nonlinear dynamical systems theory. A mathematical discrete-time model is derived using a set of basic assumptions regarding the convincement mechanisms...

We analyze a model of biological evolution recently introduced in the literature and show that punctuated equilibrium and power-law behavior arise because of the differential structural stability of the mapping between genotype and phenotype that characterizes the model. Structural stability is...

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map, exhibiting a transition from uniform to nonuniform hyperbolicity as the perturbation parameter is increased. The results for the diffusion coefficient from PO formulas agree very well with those obtained by...