Based on Lyapunov stabilization theory, this paper proposes a new generic criterion of global chaos synchronization between two coupled chaotic systems from a unidirectional linear error feedback coupling approach. The criterion is successfully applied to some typical chaotic systems with different types of nonlinearity, such as the classic Chua’s circuit, the modified Chua’s circuit with a sin...

Neural networks have been shown to be powerful tools for solving optimization problems. In this paper, we first retrospect Chen’s chaotic neural network and then propose several novel chaotic neural networks. Second, we plot the figures of the state bifurcation and the time evolution of most positive Lyapunov exponent. Third, we apply all of them to search global minima of continuous functions,...

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on h̄-scaling of an equation for time evolution of the Wigner’s quasiprobability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvat...

Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rossler oscillators only having single ̈ time-scale mechanism. Using such a multi...

A simple approach to the creation of a strange nonchaotic attractor in any chaotic system is described. The main idea is to control the parameter of the system in such a manner that the system dynamics is expanding at some times, but converging at others. With this approach, a strange nonchaotic attractor can be found in a large region in the parameter space near the boundaries between chaotic ...

This paper outlines the initial investigations on the influence of chaotic dynamics to the performance of evolutionary algorithms. The focus of this paper is the embedding of chaotic system in the form of chaos number generator for Differential Evolution. The chaotic systems of interest are the discrete dissipative systems. The twodimensional Dissipative Standard map was selected as a possible ...

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. As a system parameter changes, chaotic saddles can evolve via an infinite number of homoclinic or heteroclinic tangencies of their stable and unstable manifolds. Based on previous numerical evidence and a rigorous analysis of a class of representative models, we show that dynamical invariants suc...

Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transme...

study of the changes in the stock price in tehran stock exchange is of great importance. this is because of its application in forecasting the stock price in the stock exchange. the aim of this article is to investigate the forces and mechanisms that cause the dramatic changes in stock price and the formation of chaotic trend. to test whether the chaotic trend in the tehran stock exchange exist...

Investigating how to construct a secure hash algorithm needs in-depth study, as various existing hash functions like the MD5 algorithm have recently exposed their security flaws. At the same time, hash function based on chaotic theory has become an emerging research in the field of nonlinear information security. As an extension of our previous research works, a new chaotic iterations keyed has...