‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

Predicting future behavior of chaotic time series system is a challenging area in the literature of nonlinear systems. The prediction's accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. On the other hand the cyclic solar activity as one of the natural chaotic systems has significant effects on earth, climate, satellites and space missions. Several m...

In this paper a chaotic frequency hopping sequences generator based on dynamic quantification is proposed to address the problem of phase space reconstruction attack. This method is based on twice divisions of dynamic system interval and rotated gear dynamic quantification. Analyzed by computer simulation and statistical methods, the paper compared the performance of the proposed scheme with th...

Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron do not increase with the number of stimulations. A chaotic neuronal phase emerges at a transition to convex latency profiles which diverge exponentially, ind...

Switched systems are capable of generating chaotic multi-scroll behavior in R by means of a control signal. This signal regulates an equilibrium position of the system and is defined according to the number of scrolls that is displayed by the attractor. Thus, if two systems are controlled by different signals, they exhibit a different number of scrolls. Multistability can be created by a pair o...

Unidirectionally coupled chaotic systems hold great interest from the information processing and communications perspective. In this Letter, we report on a novel method for synchronizing two identical but internally non-homogeneous populations of chaotic maps using a scalar random coupling between them. The resulting synchronized dynamics is stochastic, and can be used in secure multi-user comm...

In this paper an algorithm for multi-color image compression-encryption is introduced. For compression step fuzzy transform based on exponential b-spline function is used. In encryption step, a novel combination chaotic system based on Sine and Tent systems is proposed. Also in the encryption algorithm, 3D shift based on chaotic system is introduced. The simulation results and security analysis...

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...