In this short note we discuss totally transitive maps. We show that all chaotic maps are not necessarily totally transitive, but there are chaotic maps with this property. Our discussion relates to symbol space Σ2 and real line.

Chaos-based communication can be applied advantageously only if the property of chaotic systems is suitably exploited. In this paper a simple non-coherent detection method for chaos-shiftkeying (CSK) modulation is proposed. Unlike the bit-energy-based detection which makes no specific use of any chaotic system property, the method proposed here exploits some distinguishable property of the two ...

Recent work on a symbolic approach to the calculation of probability distributions arising in the application of the Ott-Grebogi-Yorke strategy to transiently chaotic tent maps is extended to the case of control to a nontrivial periodic orbit. Closed forms are derived for the probability of control being achieved and the average number of iterations to control when it occurs. Both single-compon...

Let T be a tent map with the slope strictly between √ 2 and 2. Suppose that the critical point of T is not recurrent. Let K denote the inverse limit space obtained by using T repeatedly as the bonding map. We prove that every homeomorphism of K to itself is isotopic to some power of the natural shift homeomorphism.

By analyzing and researching several digital chaotic image encryption algorithms, this paper designs a symmetric image encryption scheme based on the threedimensional Henon chaotic map and the general Cat chaotic map. In this scheme, the chaotic sequence of general Cat map is used as the initialization sequence to confuse the positions of image pixels; the three-dimensional Henon chaotic map ca...

In this paper, we come up with three secure chaos-based stream ciphers, implemented on an FPGA board, for data confidentiality and integrity. To do so, first, performed the statistical security hardware metrics of certain discrete chaotic map models, such as Logistic, Skew-Tent, PWLCM, 3D-Chebyshev map, 32-bit LFSR, which are main components proposed generators. Based performance analysis colle...

‎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...