谐和激励与有界噪声作用下具有同宿和异宿轨道的Duffing振子的混沌运动

研究了具有同宿轨道、异宿轨道的双势阱Duffing振子在谐和激励与有界噪声摄动下的混沌运动.基于同宿分叉和异宿分叉，由Melnikov理论推导了系统出现混沌运动的必要条件及出现分形边界的充分条件.结果表明：当Wiener过程的强度参数大于某一临界值时，噪声增大了诱发混沌运动的有界噪声的临界幅值，相应地缩小了参数空间的混沌域，且产生混沌运动的临界幅值随着噪声强度的增大而增大.同时数值计算了最大Lyapunov指数，由最大Lyapunov指数为零从另一角度得到了系统出现混沌运动的有界噪声的临界幅值，发现在Wi 关键词： 混沌 同宿和异宿分叉 随机Melnikov方法 最大Lyapunov指数     

有界噪声和谐和激励联合作用下一类非线性系统的混沌研究

研究一类有界噪声和谐和激励联合作用下的非线性系统，首先用多尺度方法将该系统约化，针对约化后的平均系统，利用随机Melnikov过程方法结合均方值准则导出随机系统可能产生混沌运动的临界条件，结果表明在一定的参数范围内，随着Weiner过程强度参数值的增大，混沌的临界激励幅值先递减继而递增. 同时，用两类数值方法即最大Lyapunov指数法和Poincare截面法验证了解析结果. 关键词： 有界噪声 多尺度 随机Melnikov过程 混沌     

非光滑周期扰动与有界噪声联合作用下受迫Duffing系统的混沌预测

考察了一类非光滑周期扰动和有界噪声联合作用下受迫Duffing系统的动力学行为. 对于非光滑扰动项,尝试采用Fourier级数展开的方法,得到与原系统等价的光滑系统. 在此基础上给出该系统的随机Melnikov函数,由Smale马蹄理论得到系统出现混沌的解析条件,并利用Poincaré截面、相图以及最大Lyapunov指数验证了理论结果. 关键词： 非光滑系统 有界噪声 随机Melnokov函数 最大Lyapunov指数     

多频谐和与噪声作用下Flickering振子的安全盆侵蚀与混沌

研究了催化反应Flickering振子在多频率确定性谐和外力和有界随机噪声联合作用下,系统安全盆的侵蚀和混沌现象.将Melnikov方法推广到包含有限多个频率外力和随机噪声联合作用的情形,推导出了系统的随机Melnikov过程,根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值,然后用数值模拟方法计算了系统的安全盆分岔点.结果表明,由于随机扰动的影响,系统的安全盆分岔点发生了偏移,并且使得混沌容易发生.同时证明,激励频率数目的增加扩大了参数空间上的混沌区域,也使得安全盆分岔提 关键词： 多频率激励 Flickering振子 安全盆 混沌     

用多凹槽滤波器控制混沌系统

提出了一种施加多个凹槽滤波器反馈控制混沌系统的方法,使混沌运动转化为规则的运动.多凹槽滤波器控制是一种具有固定参数的线性反馈控制方法,它不影响原系统的参数,截断了系统从倍周期分叉通向混沌的道路.同时,用Melnikov方法进行理论分析,给出了合适的反馈控制器的参数.将多凹槽滤波器应用于典型的混沌系统,其仿真结果表明了该控制方法的有效性与可行性 关键词： 混沌 多凹槽滤波器 Melnikov方法     

利用凹槽滤波引导混沌系统到周期解

通过对混沌动力系统增加一个线性的反馈控制器——凹槽滤波器,引导一大类系统从混沌运动转化为期望的低周期运动.基于混沌的微扰判据——Melnikov方法,解释了该方法实现混沌控制的数学物理机理.控制仿真结果表明,该方法简单而实用,具有良好的应用前景,并能控制超混沌系统 关键词： 混沌控制 凹槽滤波 Melnikov方法     

谐和与噪声联合作用下Duffing振子的安全盆分叉与混沌

研究了软弹簧Duffing振子在确定性谐和外力和有界随机噪声联合作用下，系统安全盆的侵蚀和混沌现象.推导出系统的随机Melnikov过程，根据Melnikov过程在均方意义上出现简单零点的条件给出了系统出现混沌的临界值，然后用数值模拟方法计算了系统的安全盆分叉点.结果表明，由于随机扰动的影响，系统的安全盆分叉点发生了偏移，并且使得混沌容易发生. 关键词： Duffing振子 安全盆 分叉 混沌     

随机Bonhoeffer-Van der Pol系统的随机混沌控制

讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象，并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道，但是在随机参数及其强度的影响下也呈现出一些特点.     

一类复杂流行病学模型的混沌研究

研究了一类周期变化的非线性复杂发病率的广义流行病学模型(SIR(susceptible, infected, recovered)模型). 通过一系列坐标变换将原模型转化为Hamilton系统,运用Melnikov方法证明了该系统存在混沌运动,给出了发生同宿分岔的条件,并用数值模拟验证了上述结果. 关键词： SIR(susceptible infected recovered)模型 混沌运动 Melnikov方法 同宿分岔     

Duffing系统随机相位抑制混沌与随机共振并存现象的机理研究

针对随机相位作用的Duffing混沌系统, 研究了随机相位强度变化时系统混沌动力学的演化行为及伴随的随机共振现象. 结合Lyapunov指数、庞加莱截面、相图、时间历程图、功率谱等工具, 发现当噪声强度增大时, 系统存在从混沌状态转化为有序状态的过程, 即存在噪声抑制混沌的现象, 且在这一过程中, 系统亦存在随机共振现象, 而且随机共振曲线上最优的噪声强度恰为噪声抑制混沌的参数临界点. 通过含随机相位周期力的平均效应分析并结合系统的分岔图, 探讨了噪声对混沌运动演化的作用机理, 解释了在此过程中随机共振的形成机理, 论证了噪声抑制混沌与随机共振的相互关系.     

Temporal chaotic behaviour of vortex motion in a type-II superconductors with periodically-distributed pinning centres

Temporal chaotic character of vortex motion in systems where defects are arranged in periodic arrays has been investigated by computer simulation. Due to the high nonlinearity of the vortex–defect interaction, the temporal evolution of the vortex motion is chaotic with a power spectrum similar to what have been observed in the experiments. It is found that the strength of both the vortex–vortex and vortex–defect interactions have no significant effects on the chaotic motion of the vortices, however, the mismatch between these two interactions causes attractor crisis of the system. Different from them, the Lorentz force is not the origin of the attractor crisis, but it causes a divergent motion of the vortex (i.e., the flux flow).     

Chaotic motion of Van der Pol–Mathieu–Duffing system under bounded noise parametric excitation

The chaotic behavior of Van der Pol–Mathieu–Duffing oscillator under bounded noise is investigated. By using random Melnikov technique, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases, which is further verified by the maximal Lyapunov exponents of the system. The effect of bounded noise on Poincaré map is also investigated, in addition the numerical simulation of the maximal Lyapunov exponents.     

Oscillator with random trichotomous mass

In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable.     

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

Local control of chaotic motion

On the basis of the Ott, Grebogi and Yorke method (OGY) of controlling chaotic motion by stabilizing unstable periodic orbits we propose a control method which allows a nearly continuous adjusting of the control parameter and which therefore is capable also for controlling noisy systems. Any motion which is a solution of the system's equation of motion can be stabilized, unstable periodic orbits as well as chaotic trajectories. We demonstrate the feasibility of the method by stabilizing experimentally arbitrarily chosen chaotic trajectories of a driven damped pendulum affected by noise.     

Unstable periodic orbits and noise in chaos computing

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.     

GLOBAL CHAOS CONTROL OF NON-AUTONOMOUS SYSTEMS

This study describes a global approach of controlling chaos to reduce tedious waiting time caused by using conventional local controllers. With Euler's method, a non-autonomous system is approximated by a non-linear difference system and then an approximate global Poincaré map function is derived from the difference system by iterating one or more periods of a periodic excitation. Based on the map function, unstable periodic orbits embedded in a chaotic motion can be detected and a global controller for a targeted unstable periodic orbit is designed. The global controller makes all the unstable periodic orbits vanish except a targeted periodic orbit. Furthermore, a Lyapunov's direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit. For practical applications, system models are usually unknown. To obtain a mathematical model, non-linear system identification based on the harmonic balance principle is applied to an unknown chaotic system of a noisy environment. Simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit.     

Spectral fluctuations and 1/f noise in the order-chaos transition regime

Level fluctuations in a quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate the level fluctuations to the classical dynamics in the regular and chaotic limit. In this, we show that the spectrum of the system undergoing order to chaos transition displays a characteristic f(-gamma) noise and gamma is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles, respectively, of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.     

对称双势阱玻色-爱因斯坦凝聚系统在周期驱动下的动力学相变及其量子纠缠熵表示

研究了在对称双势阱玻色-爱因斯坦凝聚体系粒子间相互作用项上外加周期调制而引起的系统动力学相变,特别地研究了该系统通向混沌的相变过程.发现在一定驱动参数下,当外加调制频率与系统固有频率达到共振时,相平面会出现不稳定性现象,即混沌.在混沌区域,粒子在各量子态随机分布,平均布居数差在零附近波动.特别地,研究表明,混沌现象的出现可以用量子纠缠熵来表征,混沌现象出现时,两种平均纠缠熵都趋于它们的最大值. 关键词： 玻色-爱因斯坦凝聚 双势阱 混沌 纠缠熵