The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Guanrong Chen - One of the best experts on this subject based on the ideXlab platform.
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design and implementation of grid multiwing hyperchaotic Lorenz System family via switching control and constructing super heteroclinic loops
IEEE Transactions on Circuits and Systems I-regular Papers, 2012Co-Authors: Simin Yu, Jinhu Lu, Xinghuo Yu, Guanrong ChenAbstract:This paper initiates a Systematic methodology for generating various grid multiwing hyperchaotic attractors by switching control and constructing super-heteroclinic loops from the piecewise linear hyperchaotic Lorenz System family. By linearizing the three-dimensional generalized Lorenz System family at their two symmetric equilibria and then introducing the state feedback, two fundamental four-dimensional linear Systems are obtained. Moreover, a super-heteroclinic loop is constructed to connect all equilibria of the above two fundamental four-dimensional linear Systems via switching control. Under some suitable conditions, various grid multiwing hyperchaotic attractors from the real world applications can be generated. Furthermore, a module-based circuit design approach is developed for realizing the designed piecewise linear grid multiwing hyperchaotic Lorenz and Chen attractors. The experimental observations validate the proposed Systematic methodology for grid multiwing hyperchaotic attractors generation. Our theoretical analysis, numerical simulations and circuit implementation together show the effectiveness and universality of the proposed Systematic methodology.
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design and implementation of grid multiwing butterfly chaotic attractors from a piecewise Lorenz System
IEEE Transactions on Circuits and Systems Ii-express Briefs, 2010Co-Authors: Guanrong ChenAbstract:The intrinsic dynamics of the Lorenz System are confined in the positive half-space with respect to the vertical axis due to a limiting threshold effect. To break such a threshold effect, a novel piecewise Lorenz System is introduced, equipped with a staircase function and an even symmetric piecewise-linear function. The new System is autonomous, and yet, it can generate various grid multiwing butterfly chaotic attractors without requiring any external forcing. A module-based circuit is designed for implementation, with experiments reported for verification and demonstration.
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on the nonequivalence of Lorenz System and chen System
International Journal of Bifurcation and Chaos, 2010Co-Authors: Zhenting Hou, Guanrong Chen, Ning Kang, Xiangxing Kong, Guojun YanAbstract:In this paper, we prove that the Chen System with a set of chaotic parameters is not smoothly equivalent to the Lorenz System with any parameters.
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hyperchaotic attractors from a linearly controlled Lorenz System
Nonlinear Analysis-real World Applications, 2009Co-Authors: Qigui Yang, Kangming Zhang, Guanrong ChenAbstract:Abstract In this paper, a four-dimensional (4D) continuous-time autonomous hyperchaotic System with only one equilibrium is introduced and analyzed. This hyperchaotic System is constructed by adding a linear controller to the second equation of the 3D Lorenz System. Some complex dynamical behaviors of the hyperchaotic System are investigated, revealing many interesting properties: (i) existence of periodic orbit with two zero Lyapunov exponents; (ii) existence of chaotic orbit with two zero Lyapunov exponents; (iii) chaos depending on initial value w 0 ; (iv) chaos with only one equilibrium; and (v) hyperchaos with only one equilibrium. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are derived and studied.
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estimating the ultimate bound and positively invariant set for the Lorenz System and a unified chaotic System
Journal of Mathematical Analysis and Applications, 2006Co-Authors: Damei Li, Xiaoqun Wu, Junan Lu, Guanrong ChenAbstract:To estimate the ultimate bound and positively invariant set for a dynamic System is an important but quite challenging task in general. In this paper, we attempt to investigate the ultimate bound and positively invariant set for two specific Systems, the Lorenz System and a unified chaotic System. We derive an ellipsoidal estimate of the ultimate bound and positively invariant set for the Lorenz System, for all the positive values of its parameters a, b and c, and obtain the minimum value of volume for the ellipsoid. Comparing with the best results in the current literature [D. Li, J. Lu, X. Wu, G. Chen, Estimating the bounds for the Lorenz family of chaotic Systems, Chaos Solitons Fractals 23 (2005) 529–534; X. Liao, On the global basin of attraction and positively invariant set for the Lorenz chaotic System and its application in chaos control and synchronization, Sci. China Ser. E 34 (2004) 1404–1419], our new results fill up the gap of the estimate for the cases of 0
J C Sprott - One of the best experts on this subject based on the ideXlab platform.
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multistability in the Lorenz System a broken butterfly
International Journal of Bifurcation and Chaos, 2014Co-Authors: Chunbiao Li, J C SprottAbstract:In this paper, the dynamical behavior of the Lorenz System is examined in a previously unexplored region of parameter space, in particular, where r is zero and b is negative. For certain values of the parameters, the classic butterfly attractor is broken into a symmetric pair of strange attractors, or it shrinks into a small attractor basin intermingled with the basins of a symmetric pair of limit cycles, which means that the System is bistable or tristable under certain conditions. Although the resulting System is no longer a plausible model of fluid convection, it may have application to other physical Systems.
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coexisting hidden attractors in a 4 d simplified Lorenz System
International Journal of Bifurcation and Chaos, 2014Co-Authors: J C SprottAbstract:A new simple four-dimensional equilibrium-free autonomous ODE System is described. The System has seven terms, two quadratic nonlinearities, and only two parameters. Its Jacobian matrix everywhere has rank less than 4. It is hyperchaotic in some regions of parameter space, while in other regions it has an attracting torus that coexists with either a symmetric pair of strange attractors or with a symmetric pair of limit cycles whose basin boundaries have an intricate fractal structure. In other regions of parameter space, it has three coexisting limit cycles and Arnold tongues. Since there are no equilibria, all the attractors are hidden. This combination of features has not been previously reported in any other System, especially one as simple as this.
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hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz System
Nonlinear Dynamics, 2012Co-Authors: Keihui Sun, Xuan Liu, Congxu Zhu, J C SprottAbstract:This paper analyzes the hyperchaotic behaviors of the newly presented simplified Lorenz System by using a sinusoidal parameter variation and hyperchaos control of the forced System via feedback. Through dynamic simulations which include phase portraits, Lyapunov exponents, bifurcation diagrams, and Poincare sections, we find the sinusoidal forcing not only suppresses chaotic behaviors, but also generates hyperchaos. The forced System also exhibits some typical bifurcations such as the pitchfork, period-doubling, and tangent bifurcations. Interestingly, three-attractor coexisting phenomenon happens at some specific parameter values. Furthermore, a feedback controller is designed for stabilizing the hyperchaos to periodic orbits, which is useful for engineering applications.
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bifurcations and chaos in fractional order simplified Lorenz System
International Journal of Bifurcation and Chaos, 2010Co-Authors: Kehui Sun, Xia Wang, J C SprottAbstract:The dynamics of fractional-order Systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz System using the time-domain scheme. Chaos does exist in this System for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the System parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this System to yield chaos is 2.62.
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dynamics of a simplified Lorenz System
International Journal of Bifurcation and Chaos, 2009Co-Authors: Kehui Sun, J C SprottAbstract:A simplified Lorenz System with one bifurcation parameter is investigated by a detailed theoretical analysis as well as dynamic simulation, including some basic dynamical properties, Lyapunov exponent spectra, fractal dimension, bifurcations and routes to chaos. The results show that this System has complex dynamics with interesting characteristics.
Pei Yu - One of the best experts on this subject based on the ideXlab platform.
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a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Pei Yu, Xiaoxin Liao, Y L FuAbstract:Abstract In this paper, we give a constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family, which contains four independent parameters and is more general than any Lorenz Systems studied so far in the literature. The System considered in this paper not only contains the classical Lorenz System and the generalized Lorenz family as special cases, but also provides three new Lorenz Systems, which do not belong to the generalized Lorenz System, but the general Lorenz System. The results presented in this paper contain all the existing relative results as special cases.
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globally attractive and positive invariant set of the Lorenz System
International Journal of Bifurcation and Chaos, 2006Co-Authors: Pei Yu, Xiaoxin LiaoAbstract:In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz System. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz System satisfies Lipschitz condition, which is very useful in the study of chaos control and chaos synchronization. Applications are presented for globally, exponentially tracking periodic solutions, stabilizing equilibrium points and synchronizing two Lorenz Systems.
Marcus W Beims - One of the best experts on this subject based on the ideXlab platform.
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classification strategies in machine learning techniques predicting regime changes and durations in the Lorenz System
Chaos, 2020Co-Authors: Eduardo L Brugnago, Tony A Hild, Daniel Weingartner, Marcus W BeimsAbstract:In this paper, we use machine learning strategies aiming to predict chaotic time series obtained from the Lorenz System. Such strategies prove to be successful in predicting the evolution of dynamical variables over a short period of time. Transitions between the regimes and their duration can be predicted with great accuracy by means of counting and classification strategies, for which we train multi-layer perceptron ensembles. Even for the longest regimes the occurrences and duration can be predicted. We also show the use of an echo state network to generate data of the time series with an accuracy of up to a few hundreds time steps. The ability of the classification technique to predict the regime duration of more than 11 oscillations corresponds to around 10 Lyapunov times.
Qigui Yang - One of the best experts on this subject based on the ideXlab platform.
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a new 5d hyperchaotic System based on modified generalized Lorenz System
Nonlinear Dynamics, 2017Co-Authors: Qigui Yang, Meili BaiAbstract:This paper reports a new five-dimensional (5D) hyperchaotic System with three positive Lyapunov exponents, which is generated by adding a linear controller to the second equation of a 4D System that is obtained by coupling of a 1D linear System and a 3D modified generalized Lorenz System. This hyperchaotic System has very simple algebraic structure but can exhibit complex dynamical behaviors. Of particular interest are the observations that the hyperchaotic System has a hyperchaotic attractor with three positive Lyapunov exponents under a unique equilibrium, three or infinite equilibria, and there are three types of coexisting attractors of this new 5D hyperchaotic System. Numerical analysis of phase trajectories, Lyapunov exponents, bifurcation, Poincare projections and power spectrum verifies the existence of the hyperchaotic and chaotic attractors. Moreover, stability of hyperbolic or non-hyperbolic equilibria and two complete mathematical characterization for 5D Hopf bifurcation are rigorously studied. Finally, some electronic circuits are designed to implement the 5D hyperchaotic System.
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chaos in fractional conjugate Lorenz System and its scaling attractors
Communications in Nonlinear Science and Numerical Simulation, 2010Co-Authors: Qigui Yang, Caibin ZengAbstract:Chaotic dynamics of fractional conjugate Lorenz System are demonstrated in terms of local stability and largest Lyapunov exponent. Chaos does exist in the fractional conjugate Lorenz System with order less than three since it has positive largest Lyapunov exponent. Furthermore, scaling chaotic attractors of fractional conjugate Lorenz System is theoretically and numerically analyzed with the help of one-way synchronization method and adaptive synchronization method. Numerical simulations are performed to verify the theoretical analysis.
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hyperchaotic attractors from a linearly controlled Lorenz System
Nonlinear Analysis-real World Applications, 2009Co-Authors: Qigui Yang, Kangming Zhang, Guanrong ChenAbstract:Abstract In this paper, a four-dimensional (4D) continuous-time autonomous hyperchaotic System with only one equilibrium is introduced and analyzed. This hyperchaotic System is constructed by adding a linear controller to the second equation of the 3D Lorenz System. Some complex dynamical behaviors of the hyperchaotic System are investigated, revealing many interesting properties: (i) existence of periodic orbit with two zero Lyapunov exponents; (ii) existence of chaotic orbit with two zero Lyapunov exponents; (iii) chaos depending on initial value w 0 ; (iv) chaos with only one equilibrium; and (v) hyperchaos with only one equilibrium. Finally, two complete mathematical characterizations for 4D Hopf bifurcation are derived and studied.
