[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] 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.

[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] 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] A novel inverse lag synchronization is proposed, where a driven chaotic system anti-synchronizes to the past state of the driver. From observer theory, the slave system is designed. The method is tested on the famous hyperchaotic generalized Henon map and the numerical simulations fully support the analytical approach.

[en] Chaotic dynamics and synchronization of fractional-order systems have attracted much attention recently. Based on stability theory of fractional-order systems and stability theory of integer-order systems, this paper deals with the problem of coexistence of various types of synchronization between different dimensional fractional-order chaotic systems. To illustrate the capabilities of the novel schemes proposed herein, numerical and simulation results are given.

[en] A novel hash algorithm based on a spatiotemporal chaos is proposed. The original message is first padded with zeros if needed. Then it is divided into a number of blocks each contains 32 bytes. In the hashing process, each block is partitioned into eight 32-bit values and input into the spatiotemporal chaotic system. Then, after iterating the system for four times, the next block is processed by the same way. To enhance the confusion and diffusion effect, the cipher block chaining (CBC) mode is adopted in the algorithm. The hash value is obtained from the final state value of the spatiotemporal chaotic system. Theoretic analyses and numerical simulations both show that the proposed hash algorithm possesses good statistical properties, strong collision resistance and high efficiency, as required by practical keyed hash functions.

[en] Recently, there has been increasing interest in the synchronization of two chaotic systems and some significant results have been reported. In these results, a strong assumption that the two chaotic systems should be identical, i.e., without any mismatch, is imposed. Furthermore, system parameters are also assumed known exactly. Clearly, these are impractical. In this Letter, pure impulsive synchronization is considered. We quantitatively establish a relationship between a pre-specified bound of the synchronization error and the length of impulsive intervals in the presence of both parametric uncertainties and mismatch between the two systems. This is the first available result in the area, to the knowledge of the authors. With such a relationship as a guideline to choose impulsive intervals, a practical impulsive synchronization scheme is obtained. With the proposed scheme, the magnitude of the synchronization error is theoretically ensured to approach to and stay within the pre-specified bound which can be arbitrarily small. Simulation studies on the Lorenz system also verify the effectiveness of the proposed scheme

[en] In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Ši'lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type