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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
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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 下载免费PDF全文
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
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Antisynchronization of a novel hyperchaotic system with parameter mismatch and external disturbances
A novel hyperchaotic system is proposed. It is particularly interesting that the hyperchaotic system has a nonlinear term in the form of an exponential function and has only one equilibrium. Basic dynamical properties of the hyperchaotic system are investigated. Moreover, antisynchronization of the new hyperchaotic system with parameter mismatch and external disturbances is also studied in this paper by using adaptive control. Numerical simulation results further demonstrate that the proposed methods are effective and robust. 相似文献
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Liuhua Xie 《中国物理 B》2022,31(6):67103-067103
The effect of strain on charge density wave (CDW) order in $\alpha$-U is investigated within the framework of relativistic density-functional theory. The energetical stability of $\alpha$-U with CDW distortion is enhanced by the tensile strain along $a$ and $b$ axes, which is similar to the case of negative pressure and normal. However, the tensile strain along $c$ axis suppresses the energetical stability of CDW phase. This abnormal effect could be understood from the emergence of a new one-dimensional atomic chain along $c$ axis in $\alpha$-U. Furthermore, this effect is supported by the calculations of Fermi surface and phonon mode, in which the topological objects and the dynamical instability show opposite behaviors between strains along $a$/$b$ and $c$ axes. 相似文献
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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
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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
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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
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This Letter mainly concerns projective synchronization (PS) of a new hyperchaotic Lorenz system. PS with both identical and different scaling factors between two hyperchaotic Lorenz systems are realized. A general sufficient condition for PS in a certain class of chaotic (hyperchaotic) system with uncertainties is obtained by using adaptive control. Numerical simulations are performed to verify and illustrate the analytical results. 相似文献
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Chunbiao Li J. C. Sprott Wesley Thio 《Journal of Experimental and Theoretical Physics》2014,118(3):494-500
A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions. 相似文献
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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
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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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This paper presents chaos synchronization between two different
four-dimensional (4D) hyperchaotic Chen systems by nonlinear feedback
control laws. A modified 4D hyperchaotic Chen system is obtained by
changing the nonlinear function of the 4D hyperchaotic Chen system,
furthermore, an electronic circuit to realize two different 4D
hyperchaotic Chen systems is designed. With nonlinear feedback
control method, chaos synchronization between two different 4D
hyperchaotic Chen systems is achieved. Based on the stability theory,
the functions of the nonlinear feedback control for synchronization
of two different 4D hyperchaotic Chen systems is derived, the range
of feedback gains is determined. Numerical simulations are shown to
verify the theoretical results. 相似文献
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A new hyperchaotic system is presented, which has two large positive and one small negative Lyapunov exponent over a large range of parameters. As a consequence, system orbits strongly expand in some directions but rapidly shrink in some other directions. These strong expansions and shrinking lead the system orbits to be more disordered and random. Bifurcation and Poincaré-map analyses further show that the system has very rich bifurcations in different directions and extremely complicated dynamics overall. Spectral analysis shows that the system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications. 相似文献
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This paper introduces a new four-dimensional (4D) hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6. 相似文献
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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
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A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal 下载免费PDF全文
This paper proposes a new, simple and yet applicable output feedback
synchronization theorem for a large class of chaotic systems. We take a
linear combination of drive system state variables as a scale-driving
signal. It is proved that synchronization between the drive and the response
systems can be obtained via a simple linear output error feedback control.
The linear feedback gain is a function of a free parameter. The approach is
illustrated using the R\"{o}ssler hyperchaotic systems and Chua's chaotic
oscillators. 相似文献