‎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...

Recently Solak et al. [International Journal of Bifurcation and Chaos, 20 (2010), 1405–1413] cryptanalyzed the chaotic image encryption algorithm of Fridrich [International Journal of Bifurcation and Chaos, 8 (1998), 1259–1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a ...

The imbalance of the boundary energy flow due to energy injection at one end and a nonlinear van der Pol boundary condition at the other end of the spatial one-dimensional interval can cause chaotic vibration of the linear wave equation [Chen et al., 1998b, 1998c]. However, such chaotic vibration is isotropic with respect to space and time because the two associated families of characteristics ...

In the recent years, researchers developed image encryption methods based on chaotic systems. This paper proposed new image encryption technique based on new chaotic system by adding two chaotic systems: the Lorenz chaotic system and the Rössler chaotic system. The main advantage of this technique is stronger security, as is shown in the encryption tests.

-Although the motions of independent chaotic systems are uncorrelated with each other, it is possible under some conditions to synchronize a subsystem of one chaotic system with a separate chaotic system by sending a signal from the chaotic system to the subsystem. We describe here the conditions necessary for synchronization and demonstrate synchronization with a chaotic circuit.

‎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...