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[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] 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] 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] 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] 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 investigate the motion of the globally coupled maps (logistic map) driven by uniform disorder. It is shown that this disorder can produce multi-synchronization for the globally coupled chaotic maps studied by us. The disorder determines the synchronized dynamics, leading to the emergence of a wide range of new collective behaviour in which the individual units in isolation are incapable of producing in the absence of the disorder. Our results imply that the disorder can tame the collective motion of the coupled chaotic maps
[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.
[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