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[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
[en] Let be rotations on the unit circle and define as for , , where is the shift, and and are rotational angles. It is first proved that the system exhibits maximal distributional chaos for any (no assumption of ), generalizing Theorem 1 in Wu and Chen (Topol. Appl. 162:91–99, 2014). It is also obtained that is cofinitely sensitive and -sensitive and that is densely chaotic if and only if .
[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] 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] 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] Molecular motors are the workhorses of living cells. Seemingly by ‘magic’, these molecules are able to complete purposeful tasks while being immersed in a sea of thermal chaos. Here, we review the current understanding of how these machines work, present simple models based on thermal ratchets, discuss implications for statistical physics, and provide an overview of ongoing research in this important and fascinating field of study. (key issues review)
[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.