Counteracting Dynamical Degradation of Digital Chaotic Chebyshev Map via Perturbation

The chaotic map has complex dynamics under ideal conditions however it suffers from the problem of performance degradation in the case of finite computing precision. In order to prevent the dynamics degradation, in this paper the continuous Chen chaotic system is used to perturb both the inputs and parameters of Chebyshev map to minimize the chaotic degradation phenomenon under finite precision. Experimental evaluations and corresponding performance analysis demonstrate that the Chebyshev chaotic map has a good randomness and complex dynamic performance by using the proposed perturbation method, and some attributes of the proposed system are stronger than the original system (e.g. chaos attractor and approximate entropy). Finally, the corresponding pseudorandom number generator (PRNG) is constructed by this method and then its randomness is evaluated via NIST SP800-22 and TestU01 test suites, respectively. Statistical test results show that the proposed PRNG has high reliability of randomness, thus it can be used for cryptography and other potential applications.

Integer and Fractional GeneralT-System and Its Application to Control Chaos and Synchronization

We propose a three-dimensional autonomous nonlinear system, called the generalTsystem, which has potential applications in secure communications and the electronic circuit. For the generalTsystem with delayed feedback, regarding the delay as bifurcation parameter, we investigate the effect of the time delay on its dynamics. We determine conditions for the existence of the Hopf bifurcations and analyze their direction and stability. Also, the fractional order generalT-system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics of the Lyapunov coefficients are taken into consideration. The effectiveness of the chaotic control and synchronization on schemes for the new fractional order chaotic system are verified by numerical simulations.

Visualizing Research of Construction of Planar Dynamic Systems with Truncated Fourier Series

The paper constructs the planar dynamic systems with truncated Fourier series. We propose a method to generate planar tiling images of the iterative mapping with truncated Fourier series. It constructed the planar tessellations of planar dynamic systems with cyclic windows. The iterative mapping is constructed. Then we generate cyclic windows of the dynamic plane with these mappings. Filled-in Julia sets are created by generating the coordinates of any cyclic windows. The images in different windows are continuous. We can choose any cyclic windows as the basic computing region and stretch it into a square, which is transferred to the plane to compose the new form chaos attractor and filled-in Julia sets images in the Euclidian plane. Experimental results show the effectiveness of the proposed approach.

Numerical Research on Self-Sustained Oscillation and Chaos of Natural Convection in Horizontal Fluids Layer

Numerical simulation was conducted to study self-sustained oscillation and chaos of natural convection in horizontal fluids layer heated from below. The numerical simulation was conducted using SIMPLE algorithm with a QUICK scheme. Discrete time series was analyzed to study stability problem. Correlation dimension was calculated, their frequency characteristics were analyzed and chaos attractor was extracted. The results showed that oscillation appeared when Ra was over 2×104 and chaos appeared when Ra was over 5×106. When parameter was varied, chaos appeared. Strange attractor was used to describe chaos system. Fractal dimension of strange attractor was 1.19. Saturated embedding dimension of phase space reconstruction was 5. The time delay was selected for 5.

A Novel Control Method for Integer Orders Chaos Systems via Fractional-Order Derivative

A fractional-order control method is obtained to stabilize the point in chaos attractor of integer orders chaos systems. The control law has simple structure and is designed easily. Two examples are also given to illustrate the effectiveness of the theoretical result.

Associative Dynamics and Its Control of Chaotic Neural Network

In this paper, the Nagumo-Sato model is used to construct a chaotic neural network (CNN). Each reference sample is stored in the chaos attractor that is formed by the associative dynamics. When the inputs sometimes deviate obviously from its original attractive region and the correct association is not realized by itself, the feedback pinning is use to control the associative dynamics. The lost original memory will be retrieved quickly considering the fact that the CNN is a spatiotemporal system. The simulation experiments of both the associative dynamics and the retrieval process are done for the faults of broken rotor bars of an induction motor. The results show that the feedback pinning control is a simple and effective control method to the CNN.