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1.
《理论物理通讯》2015,(8)
In this paper, the Hopf bifurcation in a new hyperchaotic system is studied. Based on the first Lyapunov coefficient theory and symbolic computation, the conditions of supercritical and subcritical bifurcation in the new hyperchaotic system are obtained. Numerical simulations are used to illustrate some main results. 相似文献
2.
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. 相似文献
3.
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. 相似文献
4.
The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system 总被引:14,自引:0,他引:14
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This paper reports a new four-dimensional hyperchaotic system obtained by
adding a controller to a three-dimensional autonomous chaotic system. The
new system has two parameters, and each equation of the system has one
quadratic cross-product term. Some basic properties of the new system are
analysed. The different dynamic behaviours of the new system are studied when
the system parameter $a$ or $b$ is varied. The system is hyperchaotic in
several different regions of the parameter $b$. Especially, the two positive
Lyapunov exponents are both larger, and the hyperchaotic region is also
larger when this system is hyperchaotic in the case of varying $a$. The
hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation
diagrams and Poincar\'{e} sections. 相似文献
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Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation 总被引:1,自引:0,他引:1
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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. 相似文献
8.
A hyperchaos generated from Lorenz system 总被引:1,自引:0,他引:1
Xingyuan Wang 《Physica A》2008,387(14):3751-3758
This paper presents a four-dimension hyperchaotic Lorenz system, obtained by adding a nonlinear controller to Lorenz chaotic system. The hyperchaotic Lorenz system is studied by bifurcation diagram, Lyapunov exponents spectrum and phase diagram. Numerical simulations show that the new system’s behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the parameter varies. 相似文献
9.
In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of the equilibrium point, a Poincar map, the bifurcation diagram, and the Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective. 相似文献
10.
In this paper, a new hyperchaotic system is proposed, and the basic properties of this system are analyzed by means of equilibrium point, Poincaré map, bifurcation diagram, and Lyapunov exponents. Based on the passivity theory, the controllers are designed to achieve the new hyperchaotic system globally, asymptotically stabilized at the equilibrium point, and also realize the synchronization between the two hyperchaotic systems under different initial values respectively. Finally, the numerical simulation results show that the proposed control and synchronization schemes are effective. 相似文献
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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. 相似文献
13.
This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system, studies 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. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasi-periodic orbits. Numerical simulations are presented to show these results. 相似文献
14.
基于三阶单涡卷混沌Colpitts振荡器模型,通过引入两个分段线性三角波函数,构造了一个新型四维多涡卷超混沌系统,生成了(2M+1)×(2N+1),(2M+1)和(2N+1)涡卷混沌和超混沌吸引子.利用相轨图、Poincar啨映射、Lyapunov指数谱和分岔图等方法,对新提出的四维多涡卷超混沌系统进行了动力学分析,结果表明,多涡卷超混沌系统的Hopf分岔点仅与控制参数有关,而涡卷数量和控制参数的混沌和超混沌范围随着转折点数量的增加而增加.此外,设计了一个实现四维多涡卷超混沌系统的模拟电路,实验输出与数值仿真的两个结果基本一致. 相似文献
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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] 相似文献
17.
Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control
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Based on the three-dimensional Liu chaotic system, this paper
appends a feedback variable to construct a novel hyperchaotic Liu
system. Then, a control signal is further added to construct a novel
nonautonomous hyperchaotic Liu system. Through adjusting the
frequency of the control signal, the chaotic property of the system
can be controlled to show some different dynamic behaviors such as
periodic, quasi-periodic, chaotic and hyperchaotic dynamic
behaviours. By numerical simulations, the Lyapunov exponent
spectrums, bifurcation diagrams and phase diagrams of the two new
systems are studied, respectively. Furthermore, the synchronizing
circuits of the nonautonomous hyperchaotic Liu system are designed
via the synchronization control method of single variable coupling
feedback. Finally, the hardware circuits are implemented, and the
corresponding waves of chaos are observed by an oscillograph. 相似文献
18.
In this paper, some basic dynamical properties of a four-dimensional autonomous hyperchaotic system are investigated by means of Poincar′e mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this four-dimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback. 相似文献
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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. 相似文献