[en] The relationship between some kinds of substitutions and admissible sequences is studied. Sufficient and necessary conditions for the admissibility of the sequences generated by non-constant length substitution and constant length substitution are investigated respectively

[en] In this article, we consider a system of autonomous inductively coupled Van der Pol generators. For two coupled generators, we establish the presence of metastable chaos, a strange non-chaotic attractor, and several stable limiting cycles. Areas of parametric dependence of different modes of synchronization are obtained

No abstract available

[en] This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach

[en] This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of “chaotic region” and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a “chaotic sea” for the Nosé-Hoover oscillator

[en] Anti-synchronization between different hyperchaotic systems is presented using Lorenz and Liu systems. When the parameters of two systems are known, one can use active synchronization. When the parameters are unknown or uncertain, the adaptive synchronization is applied. The simulation results verify the effectiveness of the proposed two schemes for anti-synchronization between different hyperchaotic systems

[en] We study the dynamics of Laplacian-type coupling induced by logistic family $f_{\mu }\left(x\right)=\mu x(1-x)$, where $\mu \in [0,4]$, on a periodic lattice, that is the dynamics of maps of the form $F(x,y)=((1-\epsilon )f_{\mu }\left(x\right)+\epsilon f_{\mu }\left(y\right),(1-\epsilon )f_{\mu }\left(y\right)+\epsilon f_{\mu }\left(x\right))$ where $\epsilon >0$ determines strength of coupling. Our main objective is to analyze the structure of attractors in such systems and especially detect invariant regions with nontrivial dynamics outside the diagonal. In analytical way, we detect some regions of parameters for which a horseshoe is present; and using simulations global attractors and invariant sets are depicted.

[en] Recently, a novel block encryption system has been proposed as an improved version of the chaotic cryptographic method based on iterating a chaotic map. In this Letter, a flaw of this cryptosystem is pointed out and a chosen plaintext attack is presented. Furthermore, a remedial improvement is suggested, which avoids the flaw while keeping all the merits of the original cryptosystem

[en] Highlights: • We give an algorithm to compute regularities of SNA’s based on tools of de la Llave–Petrov. • It uses the Keller convergence construction to the attractor. • It uses Daubechies Wavelets with 16 vanishing moments. • The precision is two decimal digits compared with Weierstraß function. • The loss of regularity as parameter changes is observed from wavelet coefficients. We estimate numerically the regularities of a family of Strange Non-Chaotic Attractors related with one of the models studied in (Grebogi et al., 1984) (see also Keller, 1996). To estimate these regularities we use wavelet analysis in the spirit of de la Llave and Petrov (2002) together with some ad-hoc techniques that we develop to overcome the theoretical difficulties that arise in the application of the method to the particular family that we consider. These difficulties are mainly due to the facts that we do not have an explicit formula for the attractor and it is discontinuous almost everywhere for some values of the parameters. Concretely we propose an algorithm based on the Fast Wavelet Transform. Also a quality check of the wavelet coefficients and regularity estimates is done.

[en] Important concepts concerning tubes in dynamical systems are defined in details. In the cases of a homoclinic tube and a heteroclinically tubular cycle in autonomous systems, existence of tubular chaos is established. The main goal of this article is to stress the importance of tubes in high dimensional dynamical systems