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[en] We study the dynamics of Laplacian-type coupling induced by logistic family , where , on a periodic lattice, that is the dynamics of maps of the form where 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] The roles played by drive and response systems on generalized chaos synchronization (GS) are studied. And the generalized synchronization is classified, based on these roles, to three distinctive types: the passive GS which is mainly determined by the response system and insensitive to the driving signal; the resonant GS where phase synchronization between the drive and response systems is preceding GS; and the interacting GS where both the drive and response have influences on the status of GS. The features of these GS types and the possible changes from one types to others are investigated
[en] In [N.S. Philip, K.B. Joseph, Chaos for stream cipher, cs.CR/0102012] Philip and Joseph propose their own cipher algorithm. An efficient attack on the values of the key of this cipher is presented in this Letter. Other weaknesses of this cipher are presented, and proposals of algorithm's improvement as well
[en] Highlights: • Unraveling the bifurcation structure of a single-phase H-bridge inverter. • Demonstration of regular structures formed by persistence border-collision curves. • Detection of qualitatively different regions inside the fixed point stability domain. • Studies of the processes associated with a new route to chaos in switching systems. Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.
[en] Highlights: • Entropy of low-significance bits in digital measurements of chaos is examined. • Low-significance bits yield a two-symbol partition with a corrugated structure. • Corrugation at low-significance bits better approximates a generating partition. • Entropy rate estimation using lower-significance bits requires longer block lengths. • Considering only short block lengths can overestimate entropy of physical system. We examine the entropy of low-significance bits in analog-to-digital measurements of chaotic dynamical systems. We find the partition of measurement space corresponding to low-significance bits has a corrugated structure. Using simulated measurements of a map and experimental data from a circuit, we identify two consequences of this corrugated partition. First, entropy rates for sequences of low-significance bits more closely approach the metric entropy of the chaotic system, because the corrugated partition better approximates a generating partition. Second, accurate estimation of the entropy rate using low-significance bits requires long block lengths as the corrugated partition introduces more long-term correlation, and using only short block lengths overestimates the entropy rate. This second phenomenon may explain recent reports of experimental systems producing binary sequences that pass statistical tests of randomness at rates that may be significantly beyond the metric entropy rate of the physical source.
[en] Unstable dimension variability is an extreme form of non-hyperbolic behavior in chaotic systems whose attractors have periodic orbits with a different number of unstable directions. We propose a new mechanism for the onset of unstable dimension variability based on an interior crisis, or a collision between a chaotic attractor and an unstable periodic orbit. We give a physical example by considering a high-dimensional dissipative physical system driven by impulsive periodic forcing
[en] In this Letter, the generalized Lorenz chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Lorenz chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is given to show the effectiveness of the obtained result.
[en] In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography