舰船辐射噪声超混沌现象研究

水下弱目标探测和识别一直是水声信号处理领域中研究的难点。从Lyapunov指数谱、吸引子相空间轨迹的演化、分形维数等方面，对船舶辐射噪声是否存在超混沌现象进行了研究。实验结果表明，船舶辐射噪声信号确实存在至少两个正的Lyapunov指数，即存在超混沌现象。辐射噪声吸引子在相空间中的轨迹具有多方向伸展的趋势，且不同类型目标的吸引子具有不同的分形维数。研究结果为建立精确描述辐射噪声信号的非线性模型、为水下弱目标信号探测和识别提供一定的理论依据。     

Control and synchronize a novel hyperchaotic system

The control and hybrid projective synchronization (HPS) strategies for a novel hyperchaotic system are investigated. Firstly, the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables. Secondly, based on Lyapunov’s direct method HPS between two novel hyperchaotic systems is studied. A new nonlinear feedback vector controller is designed to guarantee HPS, which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems. Finally, numerical simulations are given to verify the effectiveness of these strategies. The proposed methods have certain significances for reducing the cost and complexity for controller implementation.     

A topological horseshoe in the hyperchaotic Rössler attractor

This Letter reports a horseshoe with two-directional expansion in the 4D hyperchaotic Rössler system. In order to show that it is indeed a horseshoe with two-dimensional expansion, some simple results on topological horseshoe which are applicable to 3D hyperchaotic maps are presented. In this way, a computer-assisted verification of hyperchaoticity is presented.     

A new hyperchaotic system and its synchronization

In this paper, a four-dimensional (4D) continuous autonomous hyperchaotic system is introduced and analyzed. This hyperchaotic system is constructed by adding a linear controller to the 3D autonomous chaotic system with a reverse butterfly-shape attractor. Some of its basic dynamical properties, such as Lyapunov exponents, Poincare section, bifurcation diagram and the periodic orbits evolving into chaotic, hyperchaotic dynamical behavior by varying parameter d are studied. Furthermore, the full state hybrid projective synchronization (FSHPS) of new hyperchaotic system with unknown parameters including the unknown coefficients of nonlinear terms is studied by using adaptive control. Numerical simulations are presented to show the effective of the proposed chaos synchronization scheme.     

二阶级联声光双稳态超浑沌的周期驱动控制

本文提出了对二阶级联声光双稳态超浑沌进行外周期激励,从而实现了对其进行有效控制.     

Revisiting the box counting algorithm for the correlation dimension analysis of hyperchaotic time series

We undertake the correlation dimension analysis of hyperchaotic time series using the box counting algorithm. We show that the conventional box counting scheme is inadequate for the accurate computation of correlation dimension (D₂) of a hyperchaotic attractor and propose a modified scheme which is automated and gives better convergence of D₂ with respect to the number of data points. The scheme is first tested using the time series from standard chaotic systems, pure noise and data added with noise. It is then applied on the time series from three standard hyperchaotic systems for computing D₂. Our analysis clearly reveals that a second scaling region appears at lower values of box size as the system makes a transition into the hyperchaotic phase. This, in turn, suggests that correlation dimension analysis can also give information regarding chaos-hyperchaos transition.     

Design and FPGA Implementation of a new hyperchaotic system

In this paper, a new four-dimensional autonomous hyperchaotic system is designed for generating complex chaotic signals. In the design, its parameters are selected according to the requirements for chaos and hyperchaos. The hyperchaotic nature is verified theoretically by using the bifurcation analysis and demonstrated experimentally by the implementation of an analogue electronic circuit. Moreover, the Field Programmable Gate Array （FPGA） technology is applied to implementing a continuous system in a digital form by using a chip of Altera Cyclone II EP2C35F484C8. The digital sequence generated from the FPGA device is observed in our experimental setup.     

A new hyperchaotic system from the Lü system and its control

This paper presents a 4D new hyperchaotic system which is constructed by a linear controller to a 3D Lü system. Some complex dynamical behaviors such as Hopf bifurcation, chaos and hyperchaos of the simple 4D autonomous system are investigated and analyzed. The corresponding hyperchaotic and chaotic attractor is first numerically verified through investigating phase trajectories, Lyapunove exponents, bifurcation path, analysis of power spectrum and Poincaré projections. Furthermore, the design is illustrated with both simulations and experiments. Finally, the control problem of a new hyperchaotic system is investigated using negative feedback control. Ordinary feedback control, dislocated feedback control and speed feedback control are used to suppress hyperchaos to an unstable equilibrium. Numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.     

Hyperchaos of four state autonomous system with three positive Lyapunov exponents

This Letter gives the results of numerical simulations of Quantum Cellular Neural Network (Quantum-CNN) autonomous system with four state variables. Three positive Lyapunov exponents confirm hyperchaotic nature of its dynamics.     

Hopf bifurcation analysis of a new modified hyperchaotic Lü system

The Hopf bifurcation of a new modified hyperchaotic Lü system with only one equilibrium is investigated in this paper. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, by applying the normal form theory, the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods are determined. In addition, numerical simulation results supporting the theoretical analysis are given.