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In the real world, every nonlinear system is inevitably affected by noise. As an example, a logistic map driven by white noise is studied. Unlike previous studies which focused on the behavior under local parameters to find analytical results, we investigate the whole driven logistic map. For a white noise driven logistic map, its nondivergent interval decreases with increasing white noise. The white noise does not change the equilibrium point and two-cycle intervals in statistics, if the driven logistic map is kept non-divergent. In particular, chaos can be excited by white noise only after the four-cycle bifurcation begins. The latest result is a necessary condition which has not been given in the literature [Int. J. Bifur. Chaos 18 (2008) 509], and it can be deduced from Sharkovsky's theorem. Numerical simulations prove these analytical results. 相似文献
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In terms of the coherent state evolution in phase space,we present a quantum mechanical version of the classical Liouville theorem.The evolution of the coherent state from |z>to|sz-rz*> corresponds to the motion from a point z(q,p) to another point sz-rz* with |s|2-|r|2=1.The evolution is governed by the so-called Fresnel operator U(s,r) that was recently proposed in quantum optics theory,which classically corresponds to the matrix optics law and the optical Fresnel transformation,and obeys group product rules.In other words,we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space,which seems to be a combination of quantum statistics and quantum optics. 相似文献
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Coherence Resonance in the System with Periodical Potential and Driven by Correlated Noises 下载免费PDF全文
YANGMing LIXiang-Lian CAOLi WUDa-Jin 《中国物理快报》2004,21(7):1220-1223
We study the ratchet model with both thermal and potential fluctuations, discussing analytically the coherence resonance of the particle moving in such a potential field. It is found that the correlation between the thermal and potential fluctuations has significant effect on the coherence of the system, i.e. negative correlation enhances the coherence of the system greatly, and with positive correlation, there appears the phenomenon that the coherence suppression and enhancement occur alternatively as the additive noise becomes larger. 相似文献
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被动行走模型只依赖重力可以在斜坡上形成自然的周期步态.当模型参数改变时,步态随之改变.应用胞映射方法与Newton-Raphson迭代结合来获取被动行走模型周期步态的不动点,消除了迭代方法在初值选取上的随机性,并获得了模型的吸引盆.通过对不同参数的模型的仿真,讨论了参数变化对步态的影响.结果表明,转动惯量增大会导致倍周期步态到混沌步态的产生,足半径减小和质心位置降低也会导致分岔的出现.
关键词:
胞映射
双足步行
倍周期
混沌 相似文献
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The behaviour of an excitable system under Gaussian white noise and external periodic forcing is systematically studied. In a large range of noise intensity, the n:l phase locking patterns are obtained for certain ranges of the input periods, where n input periods give one spike. In the phase locking regimes, the system presents low noise-to-signal ratios and shows better regularities. Out of the regimes the system behaves less regularly and the relations between the noise-to-signal ratio and the noise intensity exhibit typical stochastic resonance phenomena.At a higher noise level, the system shows the characteristic behaviour of the noise. 相似文献
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Feng-guo Li 《Central European Journal of Physics》2008,6(3):539-545
Noise can induce an inverse period-doubling transition and chaos. The effects of noise on each periodic orbit of three different
period sequences are investigated for the logistic map. It is found that the dynamical behavior of each orbit, induced by
an uncorrelated Gaussian white noise, is different in the mergence transition. For an orbit of the period-six sequence, the
maximum of the probability density in the presence of noise is greater than that in the absence of noise. It is also found
that, under the same intensity of noise, the effects of uncorrelated Gaussian white noise and exponentially correlated colored
(Gaussian) noise on the period-four sequence are different.
相似文献
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Different methods to utilize the rich library of patterns and behaviors of a chaotic system have been proposed for doing computation or communication. Since a chaotic system is intrinsically unstable and its nearby orbits diverge exponentially from each other, special attention needs to be paid to the robustness against noise of chaos-based approaches to computation. In this paper unstable periodic orbits, which form the skeleton of any chaotic system, are employed to build a model for the chaotic system to measure the sensitivity of each orbit to noise, and to select the orbits whose symbolic representations are relatively robust against the existence of noise. Furthermore, since unstable periodic orbits are extractable from time series, periodic orbit-based models can be extracted from time series too. Chaos computing can be and has been implemented on different platforms, including biological systems. In biology noise is always present; as a result having a clear model for the effects of noise on any given biological implementation has profound importance. Also, since in biology it is hard to obtain exact dynamical equations of the system under study, the time series techniques we introduce here are of critical importance. 相似文献
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本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程. 相似文献
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ZHUKai-En CHENTian-Lun BIANGuo-Xing 《理论物理通讯》2003,40(5):527-532
Two methods are presented for controlling spatiotemporal chaotic motion in coupled map lattices to a kind of periodic orbit where the dynamicM variables of all lattice sites are equM and act periodically as time evolves. Stability analysis of the periodic orbits is presented. We prove that especially the second controlling method can stabilize all the periodic orbits we concern. Basin of attraction and noise problem are discussed. 相似文献
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Two methods are presented for controlling spatiotemporal chaotic motion in coupled map lattices to a kind of periodic orbit where the dynamical variables of all lattice sites are equal and act periodically as time evolves. Stability analysis of the periodic orbits is presented. We prove that especially the second controlling method can stabilize all the periodic orbits we concern. Basin of attraction and noise problem are discussed. 相似文献
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We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that most of the out-of-phase trajectories make a transition to the in-phase state as the temperature increases. And the colored noise delays the transitions between these two dynamical states. The each curve of the average input energy per period and the phase lag versus the temperature exist a mono peak and SR appears in this system. Moreover, the optimal temperature where the SR occurs becomes larger and the region of SR grows wider as the correlation time of colored noise increases. 相似文献
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We present a control mechanism for tuning a fast-slow dynamical system undergoing a supercritical Hopf bifurcation to be in the canard regime, the tiny parameter window between small and large periodic behavior. Our control strategy uses continuous feedback control via a slow control variable to cause the system to drift on average toward canard orbits. We apply this to tune the FitzHugh-Nagumo model to produce maximal canard orbits. When the controller is improperly configured, periodic or chaotic mixed-mode oscillations are found. We also investigate the effects of noise on this control mechanism. Finally, we demonstrate that a sensor tuned in this way to operate near the canard regime can detect tiny changes in system parameters. 相似文献
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Zhen-Shu Wen 《理论物理通讯》2018,70(6):672-676
In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain the bifurcations of phase portraits of the system under different parameters conditions. Through phase portraits, we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compactons, kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions are given. Additionally, we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation, which are summarized as follows: i) We confirm that two types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system. ii) We confirm that two types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center, and the homoclinic orbit of associated system, which is tangent to the singular line at the singular point of associated system. 相似文献
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Sayat N. Akhtanov Zeinulla Zh. Zhanabaev Michael A. Zaks 《Physics letters. A》2013,377(25-27):1621-1626
We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor. 相似文献