[en] Uniform index is a conception that can describe the uniformity of a finite point set in a polyhedron, and is closely related to chaos. In order to study uniform index, the concept of contained uniform index is defined, which is similar to uniform index and has good mathematical properties. In this paper, we prove the convergence of the contained uniform index, and develop the base of proving the convergence of uniform index.

[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] 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

No abstract available

[en] Based on the generalized Lorenz system, a conjugate Lorenz-type system is introduced, which contains three different chaotic attractors, i.e., the conjugate Lorenz attractor, the conjugate Chen attractor and the conjugate Lue attractor. These new attractors are conjugate, respectively, to the Lorenz attractor, the Chen attractor and the Lue attractor in an algebraic sense. The conjugate attractors may be helpful for finally revealing the geometric structure of the Lorenz attractor.

[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

[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] In this paper, we investigate the generalized Q-S synchronization between the generalized Lorenz canonical form and the Roessler system. Firstly, we transform an arbitrary generalized Lorenz system to the generalized Lorenz canonical form, and the relation between the parameter of the generalized Lorenz system and the parameter of the generalized Lorenz canonical form are shown. Secondly, we extend the scheme present by [Yan ZY. Chaos 2005;15:023902] to study the generalized Q-S synchronization between the generalized Lorenz canonical form and the Roessler system, the more general controller is obtained. By choosing different parameter in the generalized controller obtained here, without much extra effort, we can get the controller of synchronization between the Chen system and the Roessler system, the Lue system and the Roessler system, the classic Lorenz system and the Roessler system, the Hyperbolic Lorenz system and the Roessler system, respectively. Finally, numerical simulations are used to perform such synchronization and verify the effectiveness of the controller.

[en] We have observed anti-synchronization phenomena in different chaotic dynamical systems. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Anti-synchronization problem for different chaotic dynamical systems with fully unknown parameters in response system is analyzed. This technique is applied to achieve anti-synchronization between Lorenz system, Lue system and Four-scroll system. Numerical simulations are provided to verify the effectiveness of the proposed methods.

No abstract available