Hyperchaos evolved from the Liu chaotic system

This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.     

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench (EWB). Numerical simulations are presented to show these results.     

共轭Chen混沌系统的分岔分析及基于该系统的超混沌生成研究

分析了一个三维自治混沌系统的Hopf分岔现象,该系统的混沌吸引子属于共轭Chen混沌系统.通过引入一个控制器,基于该混沌系统构建了一个四维自治超混沌系统.该超混沌系统含有一个单参数,在一定的参数范围内呈现超混沌现象.通过Lyapunov指数和分岔分析,随着参数的变化该系统轨道呈现周期轨道、准周期轨道、混沌和超混沌的演化过程. 关键词： 混沌 超混沌生成 Hopf分岔 分岔分析     

一个新的超混沌系统及其自适应追踪控制

通过在一个三维混沌系统中加入状态反馈控制器, 构造出一个新的四维超混沌系统. 分析表明, 随着不同参数变化该系统呈现周期、复杂周期、准周期、混沌及超混沌运动. 同时设计出模拟电子电路对该超混沌系统进行了实验验证. 最后, 设计了一个自适应追踪控制器,实现了其对各种不同参考信号的单变量追踪控制.     

A novel hyperchaos system only with one equilibrium

This Letter presents a new hyperchaotic system by introducing an additional state feedback into a three-dimensional quadratic chaotic system. The system only has one equilibrium, but it can evolve into periodic, quasi-periodic, chaotic and hyperchaotic dynamical behaviors. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. We find that the new hyperchaotic system possesses two big positive Lyapunov exponents within a large range of parameters. Therefore, the new hyperchaotic system may have good application prospects.     

A novel hyperchaotic system and its circuit implementation

A four-dimensional hyperchaotic system with five parameters is proposed. Its dynamical properties such as dissipativity, equilibrium points, Lyapunov exponent, Lyapunov dimension, bifurcation diagrams and Poincare maps are analyzed theoretically and numerically. Theoretical analyses and simulation tests indicate that the new system's dynamics behavior can be periodic attractor, chaotic attractor and hyperchaotic attractor as the parameter varies. Finally, the circuit of this new hyperchaotic system is designed and realized by Multisim software. The simulation results confirm that the chaotic system is different from the existing chaotic systems and is a novel hyperchaotic system. The system is recommendable for many engineering applications such as information processing, cryptology, secure communications, etc.     

状态反馈和参数调整控制离散非线性系统的倍周期分岔和混沌

利用系统的状态反馈和参数调节的方法，有效地实现了离散非线性动力系统的倍周期分岔的延迟控制和混沌吸引子中不稳定周期轨道的控制.同时，通过选择合适的调控参数，可以将系统从一个2n周期轨道控制到2m(m关键词： 状态反馈 参量调节 混沌控制 分岔控制     

Hyperchaos generated from the Lorenz chaotic system and its control

In this Letter, a hyperchaotic Lorenz system is constructed via state feedback control. Abundant dynamics of the hyperchaotic system is studied using the Lyapunov exponents, Poincaré section and bifurcation diagram. Furthermore, effective linear feedback controllers are designed for stabilizing hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbit. Numerical simulations are given to illustrate and verify the results.     

Local bifurcation analysis of a four-dimensional hyperchaotic system

Local bifurcation phenomena in a four-dlmensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.     

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.[第一段]     

THE CONTROL ACTION OF THE PERIODIC PERTURBATION ON A HYPERCHAOTIC SYSTEM

This paper presents a four-dimensional nonlinear dynamical system. By the numerical simulation the hyperchaotic attractor, Lyapunov exponents and Lyapunov dimension are obtained, also it is confirmed that hyperchaos can be driven in the system described by the equation. The control action of the periodic perturbation on the autonomous hyperchaotic system is studied, and a control rule is obtained which indicates the relationship of the control action and the frequency characteristics after degeneration of the system. Finaly the circuit implementation of the dynamical system is given.     

A new hyperchaos system and its circuit simulation by EWB

This paper reports a new hyperchaotic system evolved from the three-dimensional Lü chaotic system. The Lyapunov exponents spectrum and the bifurcation diagram of this new hyperchaotic system are obtained. Hyperchaotic attractor, periodic orbit and chaotic attractor are obtained by computer simulation. A circuit is designed to realize this new hyperchaotic system by electronic workbench.     

A novel four-dimensional autonomous hyperchaotic system

A novel four-dimensional autonomous hyperchaotic system is reported in this paper. Some basic dynamical properties of the new hyperchaotic system are investigated in detail by means of a continuous spectrum, Lyapunov exponents, fractional dimensions, a strange attractor and Poincaré mapping. The dynamical behaviours of the new hyperchaotic system are proved by not only performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment.     

平移法控制离散系统的倍周期分岔和混沌

利用平移系统的方法,实现了对离散非线性动力学系统的倍周期分岔的控制和混沌吸引子不稳定周期轨道的控制.只要选择适当的平移参数,使系统平移到不同位置,就可将系统控制在不同的预期轨道.将此方法应用到Logistic映射和Henon映射中取得了很好的控制效果.     

Analysis of transition between chaos and hyper-chaos of an improved hyper-chaotic system

An improved hyper-chaotic system based on the hyper-chaos generated from Chen's system is presented, and some basic dynamical properties of the system are investigated by means of Lyapunov exponent spectrum, bifurcation diagrams and characteristic equation roots. Simulations show that the new improved system evolves into hyper-chaotic, chaotic, various quasi-periodic or periodic orbits when one parameter of the system is fixed to be a certain value while the other one is variable. Some computer simulations and bifurcation analyses are given to testify the findings.     

A Hyperchaotic Attractor Coined from Chaotic Lü System

We report a new hyperchaotic attractor coined from the chaotic Lü system by using a state feedback controller. Theoretical analyses and simulation experiments are conducted to investigate the dynamical behaviour of the proposed hyperchaotic system     

关联可切换超混沌系统的构建与特性分析

利用拓展系统变量,增加系统的非线性函数和对原系统实施反混沌控制方法,构建了一类关联且有多种切换方式的超混沌系统,对这类系统的分岔图、平衡点的稳定性、Lyapunov指数和动力学行为的演化过程进行了分析.设计了实现切换超混沌系统的电路,利用开关的切换,一个电路能实现多个超混沌系统的功能. 关键词： 超混沌系统 切换 分岔图 Lyapunov指数     

A new hyperchaotic dynamical system

In this paper a new hyperchaotic system is reported. Some basic dynamical properties, such as continuous spectrum, Lyapunov exponents, fractal dimensions, strange attractor and Poincar\'{e} mapping of the new hyperchaotic system are studied. Dynamical behaviours of the new hyperchaotic system are proved by not only numerical simulation and brief theoretical analysis but also an electronic circuit experiment.     

模态分解法在非恒同耦合系统同步研究中的推广

通过改变耦合函数将模态分解法进行了推广,应用于非恒同耦合系统同步的研究.详细研究了周期吸引子、概周期吸引子等非恒同耦合系统的同步,得到了同步的局部渐近稳定性条件.并进行了数值模拟,发现同步时动力学现象丰富.概周期吸引子耦合系统会出现稳定的周期、概周期同步解,由于耦合周期吸引子耦合系统会出现多个稳定的周期同步解,且其吸引域差别较大,均出现了同步的多值性.同时也验证了该方法的正确性.