共查询到20条相似文献,搜索用时 656 毫秒
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Shinji Doi 《Journal of statistical physics》1989,55(5-6):941-964
Matsumoto and Tsuda studied the effects of noise on chaos in a one-dimensional Belousov-Zhabotinsky (BZ) map and found noise-induced order, that is, an external noise destroys a chaotic behavior and produces some kind of order (periodicities). This phenomenon is very interesting in understanding the relation between chaos and natural phenomena. The present paper proposes a unimodal piecewise linear map which has a flat segment. It is shown numerically that the noise-induced order can be observed in this simple map in the same way as the BZ map. These numerical results clarify the mechanism of noise-induced order. 相似文献
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We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system. 相似文献
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Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos 总被引:1,自引:0,他引:1
The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts. 相似文献
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In this paper, we report experimental evidence of Lorenz chaos for the Quincke rotor dynamics. We study the angular motion of an insulating cylinder immersed in slightly conducting oil and submitted to a direct current electric field. The simple equations which describe the dynamics of the rotor are shown to be equivalent to the Lorenz equations. In particular, we observe two bifurcations in our experimental system. Above a critical value of the electric field, the cylinder rotates at a constant rate. At a second bifurcation, the system becomes chaotic. The characteristic shape of the experimental first return map provides strong evidence for Lorenz-type chaos. 相似文献
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研究了logistic混沌映射的相关性质,指出当系统参数取值改变时,产生的混沌序列在相空间不具有遍历性.基于以上分析,构造了一种分段logistic混沌映射,对logistic映射和定义的分段logistic映射的分岔图和Lyapunov指数进行了研究,同时通过实验对这二种映射生成序列的随机性、相关系数、功率谱等性能进行了比较分析.在此基础上,定义了一种新的混沌系统性能评价指标——分岔迭代次数.结果表明,定义的分段logistic映射不仅具有良好的遍历性,而且对应的混沌系统相关评价指标的性能良好.
关键词:
混沌系统
相关系数
Lyapunov指数
功率谱 相似文献
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结合线性反馈移位寄存器(LFSR)和混沌理论各自的优点,采用循环迭代结构,给出一种将LFSR和混沌理论相结合的伪随机序列生成方法.首先根据LFSR的计算结果产生相应的选择函数,通过选择函数确定当前迭代计算使用的混沌系统,应用选择的混沌系统进行迭代计算产生相应的混沌序列;然后把生成的混沌序列进行数制转换,在将得到的二进制序列作为产生的伪随机序列输出的同时将其作为反馈值与LFSR的反馈值进行相应的运算,运算结果作为LFSR的最终反馈值,实现对LFSR生成序列的随机扰动.该方法既可生成二值伪随机序列,也可生成实值伪随机序列.通过实验对生成的伪随机序列进行了分析,结果表明,产生的序列具有良好的随机性和安全性. 相似文献
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讨论了两个非线性电路适当连接后的耦合系统随耦合强度变化的演化过程.给出了两子系统各自的分岔行为及通向混沌的过程,指出原子系统均为周期运动时,耦合系统依然会由倍周期分岔进入混沌,同时在混沌区域中存在有周期急剧增加及周期增加分岔等现象.而当周期运动和混沌振荡相互作用时,在弱耦合条件下,受混沌子系统的影响,原周期子系统会在其原先的轨道邻域内作微幅振荡,其振荡幅值随耦合强度的增加而增大,混沌的特征越加明显,相反,周期子系统不仅可以导致混沌子系统的失稳,也会引起混沌吸引子结构的变化.
关键词:
非线性电路
耦合强度
分岔
混沌 相似文献
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The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. 相似文献
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It is shown that Hamiltonian systems can exhibit the phenomenon of chaotic synchronization. Specific attention is paid to the standard map. Analytic synchronization conditions are derived and numerically verified for the standard map. We report on experimental studies of an analog electronic circuit realization of a "piecewise linear standard map." When coupled appropriately to a duplicate circuit, chaotic synchronization is observed. The relevance of this study to synchronization in other Hamiltonian systems is discussed. 相似文献
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S Rajasekar 《Pramana》1997,48(1):249-258
In this paper we consider the Bonhoeffer-van der Pol (BVP) equation which describes propagation of nerve pulses in a neural
membrane, and characterize the chaotic attractor at various bifurcations, and the probability distribution associated with
weak and strong chaos. We illustrate control of chaos in the BVP equation by the Ott-Grebogi-Yorke method as well as through
a periodic instantaneous burst. 相似文献
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Ying Zhang Gang Hu Shi Gang Chen Yugui Yao 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(1):51-57
A system of coupled master equations simplified from a model of noise-driven globally coupled bistable oscillators under periodic
forcing is investigated. In the thermodynamic limit, the system is reduced to a set of two coupled differential equations.
Rich bifurcations to subharmonics and chaotic motions are found. This behavior can be found only for certain intermediate
noise intensities. Noise with intensities which are too small or too large will certainly spoil the bifurcations. In a system
with large though finite size, the bifurcations to chaos induced by noise can still be detected to a certain degree.
Received 6 April 1999 and Received in final form 1 November 1999 相似文献
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Bambi Hu 《Physics Reports》1982,91(5):233-295
The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Hénon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent theme that underlines the importance and usefulness of such concepts as scaling, renormalization and universality. 相似文献
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通过构造一个转折点值α可变的三分段线性奇函数,研究一种新型混沌产生器.这种混沌产生器的主要特征是,随着转折点值α在0<α≤1范围内变化时,系统从倍周期分岔进 入混沌状态,可产生双层单螺旋、单层单螺旋、双层双螺旋和单层双螺旋四种不同类型的混沌吸引子,其中双层单螺旋和双层双螺旋为本电路实验中所发现的两类新型混沌吸引子.分析了这种混沌产 生器随α值在0<α≤1范围内变化时的分岔图、李雅普诺夫指数谱、最大李雅普诺夫指 数λ_max以及单层双螺旋和双层双螺旋的功率谱.在此基础上设计硬件电路,进行了计算机模拟和电路实
关键词:
混沌产生器
双层双螺旋
双层单螺旋
电路实验 相似文献
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An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized. 相似文献