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1.
This Letter presents a new three-dimensional autonomous system with four quadratic terms. The system with five equilibrium points has complex chaotic dynamics behaviors. It can generate many different single chaotic attractors and double coexisting chaotic attractors over a large range of parameters. We observe that these chaotic attractors were rarely reported in previous work. The complex dynamical behaviors of the system are further investigated by means of phase portraits, Lyapunov exponents spectrum, Lyapunov dimension, dissipativeness of system, bifurcation diagram and Poincaré map. The physical circuit experimental results of the chaotic attractors show agreement with numerical simulations. More importantly, the analysis of frequency spectrum shows that the novel system has a broad frequency bandwidth, which is very desirable for engineering applications such as secure communications. 相似文献
2.
Fox RF 《Chaos (Woodbury, N.Y.)》1995,5(4):619-633
Simple chaotic maps are used to illustrate the inherent instability of trajectory solutions to the Frobenius-Perron equation. This is demonstrated by the difference in the behavior of delta-function solutions and of extended densities. Extended densities evolve asymptotically and irreversibly into invariant measures on stationary attractors. Pointwise trajectories chaotically roam over these attractors forever. Periodic Gaussian distributions on the unit interval are used to provide insight. Viewing evolving densities as ensembles of unstable pointwise trajectories gives densities a stochastic interpretation. (c) 1995 American Institute of Physics. 相似文献
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Mohammad Saleh Tavazoei 《Physica D: Nonlinear Phenomena》2008,237(20):2628-2637
In this paper, based on the stability theorems in fractional differential equations, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system. This condition is proposed for incommensurate order systems in general, but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems. Though the presented condition is only a necessary (and not sufficient) condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system, chaotic attractors can not be observed and for what parameters and orders, the system may generate chaos. It can also be used as a tool to confirm or reject results of a numerical simulation. Some of the numerical results reported in the previous literature are confirmed by this tool. 相似文献
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Chaotic behavior of a Galerkin model of the Kolmogorov fluid motion equations is demonstrated. The study focuses on the dynamical behavior of limit trajectories branching off secondary periodic solutions. It is shown that four limit trajectories exist and transform simultaneously from periodic solutions to chaotic attractors through a sequence of bifurcations including a periodic-doubling scenario. Some instability regimes display close similarities to those of a discrete dynamical system generated by an interval map. 相似文献
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This paper proposes a saturated function series approach for generating multiscroll chaotic attractors from the fractional differential systems, including one-directional (1-D) n-scroll, two-directional (2-D) nxm-grid scroll, and three-directional (3-D) nxmxl-grid scroll chaotic attractors. Our theoretical analysis shows that all scrolls are located around the equilibria corresponding to the saturated plateaus of the saturated function series on a line in the 1-D case, a plane in the 2-D case, and a three-dimensional space in the 3-D case, respectively. In particular, each saturated plateau corresponds to a unique equilibrium and its unique scroll of the whole attractor. In addition, the number of scrolls is equal to the number of saturated plateaus in the saturated function series. Finally, some underlying dynamical mechanisms are then further investigated for the fractional differential multiscroll systems. 相似文献
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This Letter proposes a novel three-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by means of phase portraits, Lyapunov exponent spectrum, fractional dimension, bifurcation diagram and Poincaré maps of the system. The three-dimensional autonomous system is totally different from the well-known systems in previous work. The new multilayer chaotic attractors are also worth causing attention. 相似文献
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考虑原子的相干性和经典注入光场,利用随机微分方程给出非锁相条件下的Lorenz-Haken方程,研究失谐量、注入经典光场和原子相干性对非锁相Lorenz-Haken方程动力学特性的影响.在激光运转情形,失谐量造成光场位相的混沌,系统在不同条件下,出现四吸引子、双吸引子及单吸引子混沌状态,且体系的分数维维数较锁相条件下增加.光场失谐量、注入光场和原子相干性可抑制混沌.在双稳态运转下,光场位相为π的偶数倍或奇数倍,使光场稳定于正值和负值,故体系出现对称双稳态对,但无混沌状态.
关键词:
非锁相Lorenz-Haken方程
混沌
原子相干性
注入光场 相似文献
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The phase order in a one-dimensional(1 D) piecewise linear discontinuous map is investigated. The striking feature is that the phase order may be ordered or disordered in multi-band chaotic regimes, in contrast to the ordered phase in continuous systems. We carried out an analysis to illuminate the underlying mechanism for the emergence of the disordered phase in multi-band chaotic regimes, and proved that the phase order is sensitive to the density distribution of the trajectories of the attractors. The scaling behavior of the net direction phase at a transition point is observed. The analytical proof of this scaling relation is obtained. Both the numerical and analytical results show that the exponent is 1, which is controlled by the feature of the map independent on whether the system is continuous or discontinuous. It extends the universality of the scaling behavior to systems with discontinuity. The result in this work is important to understanding the property of chaotic motion in discontinuous systems. 相似文献
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In this paper, a novel first-order delay differential equation capable of generating n-scroll chaotic attractor is presented. Hopf bifurcation of the introduced n-scroll chaotic system is analytically and numerically determined. The bifurcation diagram and Lyapunov spectrum of the system are calculated and the results show that the system has a chaotic regime in a wider parameter range. Furthermore, period-3 behavior has been observed on the system. Circuit realizations of two-, three-, four-, and five-scroll chaotic attractors are also presented. 相似文献
12.
This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics. 相似文献
13.
Buncha Munmuangsaen 《Physics letters. A》2009,373(44):4038-4043
A new chaotic attractor is presented with only five terms in three simple differential equations having fewer terms and simpler than those of existing seven-term or six-term chaotic attractors. Basic dynamical properties of the new attractor are demonstrated in terms of equilibria, Jacobian matrices, non-generalized Lorenz systems, Lyapunov exponents, a dissipative system, a chaotic waveform in time domain, a continuous frequency spectrum, Poincaré maps, bifurcations and forming mechanisms of its compound structures. 相似文献
14.
利用Silnikov定理,讨论了具有自动频率跟踪功能电磁振动机械系统的混沌特性.借助卡尔达诺公式和微分方程组级数解分别讨论了该系统的特征值问题和同宿轨道的存在性,进而比较严密地证明了该系统Silnikov型Smale混沌的存在性,并给出发生Silnikov型Smale混沌所需条件.利用数值模拟得到该类机电耦合系统的相轨迹图、Lyaponov指数谱和Lyaponov维数,进一步验证了该非线性系统存在奇怪吸引子.
关键词:
混沌系统
Lyapunov指数
Silnikov定理
耦合 相似文献
15.
We numerically investigate the boundary-induced spiral wave drift in the complex Ginzburg–Landau equation. We find some novel phenomena for the spiral drifting dynamics such as the chaotic behaviors, the transient chaos and asymmetrical attractors. 相似文献
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In chemical reaction process, mathematical modeling of certain experiments lead to Brusselator system of equations. In this article, the dynamical behaviors of reaction Brusselator system with fractional Caputo derivative is studied. Also, Its stability and chaotic attractors of the commensurate fractional dynamical Brussleator system are discussed. The fractional derivative operators are nonlocal and having weak singularity as compare to the classical derivative operators. To find the analytical solutions of fractional dynamical systems is a big challenge, therefore, new techniques are worth demanding to solve such problems. To overcome this difficulty, the optimal homotopy asymptotic method is extended in this study to the system of fractional partial differential equations. A numerical example is presented as well to investigate the convergence, performance, and effectiveness of this method. 相似文献
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Novel four-dimensional autonomous chaotic system generating one-, two-, three- and four-wing attractors
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In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincaré map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations are in good agreement with the numerical simulation results. 相似文献
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The object of this paper is to reveal the relation between dynamics of the fractional system and its dimension defined as a sum of the orders of all involved derivatives. We take the fractional Lorenz system as example and regard one or three of its orders as bifurcation parameters. In this framework, we compute the corresponding bifurcation diagrams via an optimal Poincaré section technique developed by us and find there exist two routes to chaos when its dimension increases from some values to 3. One is the process of cascaded period-doubling bifurcations and the other is a crisis (boundary crisis) which occurs in the evolution of chaotic transient behavior. We would like to point out that our investigation is the first to find out that a fractional differential equations (FDEs) system can evolve into chaos by the crisis. Furthermore, we observe rich dynamical phenomena in these processes, such as two-stage cascaded period-doubling bifurcations, chaotic transients, and the transition from coexistence of three attractors to mono-existence of a chaotic attractor. These are new and interesting findings for FDEs systems which, to our knowledge, have not been described before. 相似文献