Statistical periodicity is a statistical property of densities which arises in the description of retarded dynamical systems. This property is particularly attractive as a possible mechanism for the ensemble coding of information in the nervous system because it operates rapidly and has high storage capacity. For a population of neurons which exhibits statistical periodicity, information would ...

is a skew-symmetric matrix. Equation (1.1) is known as the Toda lattice. Among many of its interesting properties which have been studied [2-4, 7, 111, probably the most important features are the isospectral property-starting with any initial value L(0) = Lo, the solution flow L(f) of (1.1) has the same spectrum for all r, and the global asymptotic convergence property-the solution flow L(t), ...

The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has po...

The Beijing road traffic system, as a typical huge urban traffic system, provides a platform for analyzing the complex characteristics and the evolving mechanisms of urban traffic systems. Based on dynamic network theory, we construct the dynamic model of the Beijing road traffic system in which the dynamical properties are described completely. Furthermore, we come into the conclusion that urb...

A basin of attraction represents the set initial conditions leading to a specific asymptotic state given dynamical system. Here, we provide classification most common basins found in nonlinear dynamics with help entropy. We have also interesting connections between entropy and other measures used characterize unpredictability associated attraction, such as uncertainty exponent, lacunarity or di...

We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly. We use this technique to estimate the complexity function for genomes of several organisms under the assumption that a genome is a sequence produced by a (u...

Enhancing the synchronization of dynamical networks is of great interest to those designing and analyzing many man-made and natural systems. In this work, we investigate how network topology can be evolved to improve this property through the rewiring of edges. A computational tool called NETEVO performs this task using a simulated annealing metaheuristic. In contrast to other work which consid...

Most philosophical accounts of emergence are based on supervenience, with supervenience being an ontologically synchronic relation of determination. This conception of emergence as a relation of supervenience, I will argue, is unable to make sense of the kinds of emergence that are widespread in selforganizing and nonlinear dynamical systems, including distributed cognitive systems. In these dy...