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[en] Recently, Ranjan proposed a novel public key encryption technique based on multiple chaotic systems [Phys Lett 2005;95]. Unfortunately, Wang soon gave a successful attack on its special case based on Parseval's theorem [Wang K, Pei W, Zhou L, et al. Security of public key encryption technique based on multiple chaotic system. Phys Lett A, in press]. In this letter, we give an improved example which can avoid the attack and point out that Wang cannot find the essential drawback of the technique. However, further experimental result shows Ruanjan's encryption technique is inefficient, and detailed theoretic analysis shows that the complexity to break the cryptosystem is overestimated
[en] Highlights: • Corron et al. developed a chaotic system whose signal could be described by a linear combination of basis functions. • They were able to build a matched filter for their system. • This paper uses the ideal of basis functions generated by an unstable circuit. • The basis functions are easily made orthogonal, allowing for multiplexing and matched filtering. • The receiver is implemented in an experiment as an analog circuit, allowing for a very simple design. - Abstract: Work by Corron et al. [1,2] represented a chaotic signal as a set of basis functions, and built a matched filter for the resulting signal. This paper makes use of basis functions without an underlying chaotic system. Matched filtering is still possible, allowing communication in noisy environments, but the resulting signals can be broad band, which is useful for producing signals that are hard to detect. The receiver design retains the simplicity of Corron et al. [1,2], which is good when weight, power consumption or bandwidth are constraints on the receiver.
[en] The concept of A-coupled-expanding maps is one of the more natural and useful ideas generalized from the horseshoe map which is commonly known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behavior. In this paper, we focus on the relationship between A-coupled-expanding and distributional chaos. We prove two theorems which give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an m × m irreducible transition matrix
[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] The grey prediction of Lorenz chaotic system will be discussed carefully in this paper. We are mainly using GM(1,1) model to predict data sequences, and the usual prediction precision has exceeded 90%. In the symbolic prediction of Lorenz chaotic dynamical system, the precision of grey prediction certainly will decrease as the length of symbolic sequence is increasing. But in this place we have found a generating rule that may realize chaotic synchronization at least in a short and medium term, and we can analysis and predict in this way.
[en] Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme seems useful and good. In addition, we discuss some issues which can be important to interdisciplinary education in physics: for example the possible difficulties in programme design, the expertise barriers of non-major fields, the role of non-theoretical education in understanding and the project-type team activities
[en] This paper proposes a novel particle swarm optimization (PSO) algorithm, chaotically encoded particle swarm optimization algorithm (CENPSOA), based on the notion of chaos numbers that have been recently proposed for a novel meaning to numbers. In this paper, various chaos arithmetic and evaluation measures that can be used in CENPSOA have been described. Furthermore, CENPSOA has been designed to be effectively utilized in data mining applications.
[en] We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system
[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.