共查询到20条相似文献,搜索用时 15 毫秒
1.
Li-Ping Zhang 《中国物理 B》2022,31(3):30503-030503
This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov (Kaplan—Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work. 相似文献
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A novel 5-dimensional(5D) memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones. 相似文献
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This paper introduces a four-dimensional(4D) segmented disc dynamo which possesses coexisting hidden attractors with one stable equilibrium or a line equilibrium when parameters vary. In addition, by choosing an appropriate bifurcation parameter, the paper proves that Hopf bifurcation and pitchfork bifurcation occur in the system. The ultimate bound is also estimated. Some numerical investigations are also exploited to demonstrate and visualize the corresponding theoretical results. 相似文献
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This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability. 相似文献
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We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation equations with Z2×Z2 symmetry are derived. A local analysis of solutions is then considered, including the derivation of conditions for a tertiary Hopf bifurcation. Applications to symmetrically coupled maps and to two coupled, vertically forced pendulums are described. 相似文献
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<正>To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with the differential Chay model,this paper fits a discontinuous map of a slow control variable of the Chay model based on simulation results.The procedure of period adding bifurcation scenario from period k to period k + 1 bursting(k = 1,2,3,4) involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map.Moreover,dynamics of the border-collision bifurcation are identified in the discontinuous map,which is employed to understand the experimentally observed period increment sequence.The simple discontinuous map is of practical importance in the modeling of collective behaviours of neural populations like synchronization in large neural circuits. 相似文献
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We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation
phenomenon in discontinuous systems is presented. We establish that whenever the elements of ann-cycle (n > 1) approach the discontinuities of thenth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease
in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors.
Our results are verified by numerical experiments as well. 相似文献
10.
Jesus M. Munoz-Pacheco Christos Volos Fernando E. Serrano Sajad Jafari Jacques Kengne Karthikeyan Rajagopal 《Entropy (Basel, Switzerland)》2021,23(7)
In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system. 相似文献
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Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically. 相似文献
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由两个一维抛物线离散映射作推广并非线性耦合,实现了一个新的二维抛物线离散映射.利用不动点稳定性分析和映射分岔分析,研究了所提出的二维离散映射的复杂动力学行为及其吸引子的演变过程,阐述了它所特有的共存分岔模式和快慢周期振荡效应等动力学特性.研究结果表明:二维抛物线离散映射具有动力学特性调节和动态幅度调节的两个功能不同的控制参数,存在Hopf分岔、分岔模式共存、锁频和周期振荡快慢效应等非线性物理现象.并基于微控制器实现的数字电路验证了相应的理论分析和数值仿真结果.关键词:二维离散映射分岔吸引子参数 相似文献
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Laura Tedeschini-Lalli 《Journal of statistical physics》1982,27(2):365-388
A two-parameter family of nonlinear differential equations x=F(x, R, ) is studied, which allows one to connect continuously, as varies from zero to one, the different phenomenologies exhibited by a model of 5-mode truncated Navier-Stokes equations and by a 7-mode one extending it. A critical value is found for, at which the most significant phenomena of the 5-mode system either vanish or go to infinity. New phenomena arise then, leading to the 7-mode model.Supported by G.N.F.M., C.N.R. 相似文献
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Nadjette Debbouche Shaher Momani Adel Ouannas Mohd Taib Shatnawi Giuseppe Grassi Zohir Dibi Iqbal M. Batiha 《Entropy (Basel, Switzerland)》2021,23(3)
This article investigates a non-equilibrium chaotic system in view of commensurate and incommensurate fractional orders and with only one signum function. By varying some values of the fractional-order derivative together with some parameter values of the proposed system, different dynamical behaviors of the system are explored and discussed via several numerical simulations. This system displays complex hidden dynamics such as inversion property, chaotic bursting oscillation, multistabilty, and coexisting attractors. Besides, by means of adapting certain controlled constants, it is shown that this system possesses a three-variable offset boosting system. In conformity with the performed simulations, it also turns out that the resultant hidden attractors can be distributively ordered in a grid of three dimensions, a lattice of two dimensions, a line of one dimension, and even arbitrariness in the phase space. Through considering the Caputo fractional-order operator in all performed simulations, phase portraits in two- and three-dimensional projections, Lyapunov exponents, and the bifurcation diagrams are numerically reported in this work as beneficial exit results. 相似文献
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利用荷控忆阻器和一个电感串联设计一种新型浮地忆阻混沌电路.用常规动力学分析方法研究该系统的基本动力学特性,发现系统可以产生一对关于原点对称的\"心\"型吸引子.将观察混沌吸引子时关注的电压、电流推广到功率和能量信号,观察到蝴蝶结型奇怪吸引子的产生.理论分析Hopf分岔行为并通过数值仿真进行验证,结果表明系统随电路参数变化能产生Hopf分岔、反倍周期分岔两种分岔行为.相对于其它忆阻混沌电路该电路采用的是一个浮地型忆阻器,并且在初始状态改变时,能产生共存吸引子和混沌吸引子与周期极限环共存现象. 相似文献
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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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Dynamical behaviors of a class-B laser system with dissipative strength are analyzed for a model in which the polarization is adiabatically eliminated. The results show that the injected signal has an important effect on the dynamical behaviors of the system. When the injected signal is zero, the dissipative term of the class-B laser system is balanced with external interference, and the quasi-periodic flows with conservative phase volume appear. And when the injected signal is not zero, the stable state in the system is broken, and the attractors (period, quasi-period, and chaos) with contractive phase volume are generated. The numerical simulation finds that the system has not only one attractor, but also coexisting phenomena (period and period, period and quasi-period) in special cases. When the injected signal passes the critical value, the class-B laser system has a fold-Hopf bifurcation and exists torus \"blow-up\" phenomenon, which will be proved by theoretical analysis and numerical simulation. 相似文献
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In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image
encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are
obvious. In this paper, permutation and substitution methods are incorporated to present a stronger image encryption algorithm.
Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the cipher-image
and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages
of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.
Supported by the National Natural Science Foundation of China (Grant No. 60874009) and the Foundation for the Author of National
Excellent Doctoral Dissertation of China (Grant No. 200444) 相似文献