Conventional generalized polynomial chaos is known to fail for long time integration, loosing its optimal convergence behaviour and developing unacceptable error levels. The reason for this loss of convergence is the assumption that the probability density function is constant in time. By allowing a probability density function to evolve in time the optimal properties of polynomial chaos are re...

Neural networks are dense in the space of dynamical systems. We present a Monte Carlo study of the dynamic properties along the route to chaos over random dynamical system function space by randomly sampling the neural network function space. Our results show that as the dimension of the system (the number of dynamical variables) is increased, the probability of chaos approaches unity. We prese...

In chaos-based communication systems, parameter variation in the chaos generator and additive channel noise represent two practical problems that are hard to sol*. For chaos-based digital communication, non-coherent detection has the advantage that the receiver does not need to reproduce the same chaos basis function that has been generated in the transmitter. SUC h reproduction typically requi...

This paper presents a fuzzy controller to solve a master-slave chaos synchronization problem. At first, the method of traditional sliding mode control is considered, which utilizes the discontinuous sign function to make the system state reaching a sliding surface. Next, fuzzy rules are determined according to the Lyapunov theorem, and the fuzzy controller is designed for chaos synchronization....

We propose manifold piecewise constant systems (ab. MPC) and consider basic phenomena: the 2-D, 3-D and 4-D MPCs exhibit limit-cycle, line-expanding chaos and areaexpanding chaos, respectively. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewise-linear return map which can be expressed explicitly. In order to analyze the p...

This contribution presents the results of an investigation on deterministic spatiotemporal chaos control by means of evolutionary algorithms. Three evolutionary algorithms are used for chaos control: differential evolution, self-organizing migrating algorithm and genetic algorithm. Models of spatiotemporal chaos, so called coupled map lattices, are used. The main aim of this investigation was t...

This contribution introduces an investigation on deterministic spatiotemporal chaos control based on evolutionary algorithms use. Two evolutionary algorithms are used for chaos control here: differential evolution and self-organizing migrating algorithm. Like a model of spatiotemporal chaos so called coupled map lattices are used. Main aim of this investigation was to show that evolutionary alg...

This paper examines the most probable route to chaos in high-dimensional dynamical systems function space (time-delay neural networks) endowed with a probability measure in a computational setting . The most probable route to chaos (relative to the measure we impose on the function space) as the dimension is increased is observed to be a sequence of Neimark-Sacker bifurcations into chaos. The a...