共查询到20条相似文献,搜索用时 15 毫秒
1.
通过对一个五维超混沌系统施加平移变换、镜像映射和滞回切换操作,将多翼混沌吸引子结构由双翼倍增为四翼.施加n-1次相似操作可以得到2n翼的超混沌吸引子.设计了一个简单的电路实现吸引子翼数量的倍增.该方法在保留了系统原有超混沌特性的基础上,增加了吸引子的拓扑结构复杂性,使之更适合保密通信等领域的应用.
关键词:
多涡卷吸引子
多翼吸引子
超混沌系统 相似文献
2.
提出了一种构造多翼蝴蝶混沌吸引子的新方法,在Liu混沌系统的基础上,通过设计一种新的分段线性函数,构造了一个产生多翼蝴蝶混沌吸引子的混沌系统,对系统的平衡点、Lyapunov指数谱、分岔图、相图、频谱和Poincare截面进行了分析。最后,设计了相应的硬件电路,电路实验结果与数值仿真结果一致,验证了该方法的可行性和有效性。 相似文献
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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
6.
Novel four-dimensional autonomous chaotic system generating one-, two-, three- and four-wing attractors 下载免费PDF全文
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
7.
Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium 下载免费PDF全文
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
8.
对于具有隐藏吸引子的混沌系统,既有文献大多只针对整数阶系统进行分析与控制研究.基于Sprott E系统,构建了仅有一个稳定平衡点的分数阶混沌系统,通过相位图、Poincare映射和功率谱等,分析了该系统的基本动力学特征.结果显示,该系统展现出了丰富而复杂的动力学特性,且通过随阶次变化的分岔图可知,系统在不同阶次下呈现出周期运动、倍周期运动和混沌运动等状态,这些动力学特征对于保密通信等实际工程领域有重要的研究价值.针对该具有隐藏吸引子的分数阶系统,应用分数阶系统有限时间稳定性理论设计控制器,对系统进行有限时间同步控制,并通过数值仿真验证了其有效性. 相似文献
9.
Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors 下载免费PDF全文
《中国物理 B》2021,30(10):100506-100506
A five-value memristor model is proposed, it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current. Then, based on the classical Liu–Chen system, a new memristor-based four-dimensional(4D) chaotic system is designed by using the five-value memristor. The trajectory phase diagram, Poincare mapping, bifurcation diagram, and Lyapunov exponent spectrum are drawn by numerical simulation. It is found that, in addition to the general chaos characteristics, the system has some special phenomena, such as hidden homogenous multistabilities, hidden heterogeneous multistabilities, and hidden super-multistabilities. Finally, according to the dimensionless equation of the system, the circuit model of the system is built and simulated. The results are consistent with the numerical simulation results, which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper. 相似文献
10.
Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor 下载免费PDF全文
Li-Ping Zhang 《中国物理 B》2022,31(10):100503-100503
We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction, bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multi-stability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially, this work can be used for some real applications in secure communication, such as data and image encryptions. 相似文献
11.
A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control 下载免费PDF全文
This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors' knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach. 相似文献
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Atiyeh Bayani Karthikeyan Rajagopal Abdul Jalil M. Khalaf Sajad Jafari G.D. Leutcho J. Kengne 《Physics letters. A》2019,383(13):1450-1456
Analyzing chaotic systems with coexisting and hidden attractors has been receiving much attention recently. In this article, we analyze a four dimensional chaotic system which has a plane as the equilibrium points. Also this system is of the group of systems that have coexisting attractors. First, the system is introduced and then stability analysis, bifurcation diagram and Largest Lyapunov exponent of this system are presented as methods to analyze the multistability of the system. These methods reveal that in some ranges of the parameter, this chaotic system has three different types of coexisting attractors, chaotic, stable node and limit cycle. Some interesting dynamics properties such as reversals of period doubling bifurcation and offset boosting are also presented. 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
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This paper proposes a novel approach for generating a multi-scroll
chaotic system. Together with the theoretical design and numerical
simulations, three different types of attractor are available,
governed by constructing triangular wave, sawtooth wave and
hysteresis sequence. The presented new multi-scroll chaotic system
is different from the classical multi-scroll chaotic Chua system in
dimensionless state equations, nonlinear functions and maximum
Lyapunov exponents. In addition, the basic dynamical behaviours,
including equilibrium points, eigenvalues, eigenvectors,
eigenplanes, bifurcation diagrams and Lyapunov exponents, are
further investigated. The success of the design is illustrated by
both numerical simulations and circuit experiments. 相似文献
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Nonlinear dynamics of the time-delayed Mackey-Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincare section. Synchronizations of the drive-response Mackey-Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found. 相似文献
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Whether Wada basins of strange nonchaotic attractors (SNAs) can exist has been an open problem. Here we verify the existence of Wada basin for SNAs in a quasiperiodically forced Duffing map. We show that the SNAs? basins are full Wada for a set of parameters of positive measure. We identify two types of SNAs? Wada basins by the basin cell method. It suggests that SNAs cannot be predicted reliably for the specific initial conditions. 相似文献
17.
Dynamics analysis of a 5-dimensional hyperchaotic system with conservative flows under perturbation 下载免费PDF全文
《中国物理 B》2021,30(10):100502-100502
Conservative chaotic flows have better ergodicity, therefore researching dynamics and applications of conservative systems has become a hot topic. We introduce a constant-perturbation into a 5-dimensional(5D) conservative model.Consequently, the line equilibria of original model have been changed to non-equilibrium. Plentiful chaos phenomena such as coexisting conservative flows can be observed in this modified system. In addition, by increasing the magnitude of the disturbance, the conservative system can be transformed to a dissipative system. Then, the modified system is realized by an xc7z020clg400 field programmable gate array(FPGA) chip. The designed chaotic oscillator consumes fewer resources and has high iteration speed. Finally, a pseudo random number generator based on this novel digital oscillator is designed. 相似文献
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Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap 下载免费PDF全文
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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Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system 下载免费PDF全文
A new four-dimensional quadratic smooth autonomous chaotic
system is presented in this paper, which can exhibit periodic orbit
and chaos under the conditions on the system parameters.
Importantly, the system can generate one-, two-, three- and
four-scroll chaotic attractors with appropriate choices of
parameters. Interestingly, all the attractors are generated only by
changing a single parameter. The dynamic analysis approach in the
paper involves time series, phase portraits, Poincar\'{e} maps,
a bifurcation diagram, and Lyapunov exponents, to investigate some
basic dynamical behaviours of the proposed four-dimensional system. 相似文献
20.
Generation of countless embedded trumpet-shaped chaotic attractors in two opposite directions from a new three-dimensional system with no equilibrium point 下载免费PDF全文
A new three-dimensional(3D) continuous autonomous system with one parameter and three quadratic terms is presented firstly in this paper. Countless embedded trumpet-shaped chaotic attractors in two opposite directions are generated from the system as time goes on. The basic dynamical behaviors of the strange chaotic system are investigated. Another more complex 3D system with the same capability of generating countless embedded trumpet-shaped chaotic attractors is also put forward. 相似文献