Iterated function systems make up an interesting class of stochastic processes which are useful for many types of stochastic modeling. In this paper we review and slightly generalize a contractivity condition guaranteeing uniqueness of invariant measures. Also, we examine how the invariant...

The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun's studies. In particular the so called Okun's Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables...

We study the dynamical behavior of vehicular traffic through a series of traffic signals. The vehicular traffic is controlled with the use of the cycle time generated by a logistic map. Each signal changes periodically with a cycle time, and the cycle time varies from signal to signal. The...

Dynamic behaviours of the 2∞ attractor at the accumulation of period doubling in the logistic map are studied by the sum of the local expansion rates Sn(x1) of nearby orbits. The variance 〈[Sn(x)]2〉 and algebraic exponent ßn(x1) = Sn(x1)/ln(n) exhibits self-similar structures. The...

We study the synchronization of a coupled map lattice consisting of a one-dimensional chain of logistic maps. We consider global coupling with a time-delay that takes into account the finite velocity of propagation of interactions. We recently showed that clustering occurs for weak coupling,...

We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a ring-type with a central node) and two random...

As a continuous opinion dynamics model, the information accumulation system (IAS) includes three basic mechanisms of the news, the inheritance and the diffusion as contributing to the information accumulation process of a system. A system is composed of agents who diffuse information through...

Avalanche or cascade failure is ubiquitous. We first classify the cascading phenomena into two categories: the cascading disasters which result in large-scale functional failures and the cascading events that do not lead to disasters. We elucidate that two important factors, the increasing...

The transition from a non-chaotic state to a chaotic state is a commonly concerned issue in the study of coupled dynamical networks. In this work, we consider a network consisting of nodes that are in non-chaotic states with parameters in non-chaotic regions before they are coupled together. We...

We extend existing studies of weakly sensitive points within the framework of Tsallis non-extensive thermodynamics to include weakly insensitive points at the edge of chaos. Analyzing tangent points of the logistic map we have verified that the generalized entropy with suitable entropic index q...