耦合发电机系统的分岔和双参数特性

在综合分析系统基本动力学特性的基础上,通过数值计算Lyapunov指数谱、分岔图等,讨论了耦合发电机系统的混沌分岔行为和周期窗口的性态变化;计算和分析了系统在二维参数空间的双参数特性.结果显示系统在倍周期分岔中会出现缺边现象,在双参数空间系统出现复杂的分岔结构,两个控制参数对系统动力学行为的影响特性有所差别. 关键词： 耦合发电机系统 分岔 周期窗口 双参数特性     

损耗型变形耦合电机系统的混沌参数特性

提出一种考虑两种损耗特性的耦合发电机模型. 与原来的耦合发电机模型相比, 该模型更能反映实际情况. 通过数值计算Lypunov指数谱、分岔图、Poincaré映射等, 分析了系统在各种参数空间的性态变化. 结果显示考虑机械阻尼损耗的耦合发电机模型具有双吸引子, 机械阻尼损耗一方面可以抑制系统混沌, 另一方面却使系统在参数空间具有更复杂的混沌特性, 表征这两种损耗特性的参数对系统动力学行为都有显著的影响.     

周期切换下Rayleigh振子的振荡行为及机理

本文研究了自治与非自治电路系统在周期切换连接下的动力学行为及机理.基于自治子系统平衡点和极限环的相应稳定性分析和切换系统李雅普诺夫指数的理论推导及数值计算.讨论了两子系统在不同参数下的稳态解在周期切换连接下的复合系统的各种周期振荡行为,进而给出了切换系统随参数变化下的最大李雅普诺夫指数图及相应的分岔图,得到了切换系统在不同参数下呈现出周期振荡,概周期振荡和混沌振荡相互交替出现的复杂动力学行为并分析了其振荡机理.给出了切换系统通过倍周期分岔,鞍结分岔以及环面分岔到达混沌的不同动力学演化过程.     

切换电路系统的振荡行为及其非光滑分岔机理

探讨了周期时间开关及控制阈值下在两个Rayleigh型子系统之间切换的电路系统随参数变化的复杂动力学演化过程, 通过对子系统平衡点的分析, 给出了参数空间中Fold分岔和Hopf分岔的条件, 考察了切换面处广义Jacobian矩阵特征值随辅助参数变化的分布情况, 得到了切换面处系统可能存在的各种分岔行为, 进而讨论了系统不同行为的产生机理, 指出系统的相轨迹存在分别由周期开关和控制阈值决定的两类不同的分界点, 而系统轨迹与非光滑分界面的多次碰撞将导致系统由周期倍化分岔导致混沌振荡.     

分段Filippov系统的簇发振荡及擦边运动机理

本文旨在揭示非光滑Filippov系统中由频域上不同尺度耦合导致的簇发振荡行为及其产生机理.以经典的周期激励Duffing振子为例,通过引入对状态变量的分段控制及适当选取参数,使得激励频率与系统固有频率之间存在量级差距,建立了频域两尺度耦合的Filippov系统.当激励频率远小于系统的固有频率时,可以将整个激励项视为慢变参数或慢变子系统,从而得到广义自治快子系统.分析了由非光滑分界面划分的不同区域中各快子系统的平衡点及其分岔特性随慢变参数变化的演化过程.考察了两种典型参数条件下系统的振荡行为及其动力学特性,指出参数变化不仅会引起其相应子系统平衡曲线及其分岔特性的改变,也会导致不同模式的簇发振荡.同时,轨迹穿越非光滑分界面时会产生不同的动力学行为,特别是在一定参数条件下,由于运动轨迹受不同子系统的交替控制,存在着擦边运动现象,从而导致特殊形式的非光滑簇发振荡.基于转换相图及各区域中快子系统的平衡曲线及其分岔特性,揭示了非光滑分界面对系统簇发振荡的影响规律及不同簇发振荡的分岔机理.     

一种时延范德波尔电磁系统中的复杂行为(Ⅰ)——分岔与混沌现象

建立了一种可积的无穷维系统——时延范德波尔电磁系统，采用Poincaré映射分析了系统随参数E和λ变化发生的分岔与混沌现象，发现这种时延系统具有复杂的非线性动力学特性，例如吸引子共存、间歇性混沌、类似边界碰撞分岔通向混沌以及周期增加的现象.在研究系统时间混沌行为的同时，还对空间混沌行为进行了初步分析，通过描绘空间分布图发现时延范德波尔电磁系统随参数E和λ变化时，在空间中会呈现出周期和混沌等不同的图案. 关键词： 分岔 混沌 无穷维系统 时延范德波尔电磁系统     

非线性切换系统的动力学行为分析

建立了周期切换下的非线性电路模型,基于子系统平衡点及其稳定性分析,分别给出了其相应的fold分岔和Hopf分岔条件,讨论了子系统在不同平衡态下由周期切换导致的各种复杂行为,指出切换系统的周期解随参数的变化存在着倍周期分岔和鞍结分岔两种失稳情形,并相应地导致不同的混沌振荡,进而结合系统轨迹及其相应的分岔分析,揭示了各种振荡模式的动力学机理. 关键词： 周期切换 倍周期分岔 鞍结分岔 混沌     

耦合相振子系统同步的序参量理论

节律行为,即系统行为呈现随时间的周期变化,在我们的周围随处可见.不同节律之间可以通过相互影响、相互作用产生自组织,其中同步是最典型、最直接的有序行为,它也是非线性波、斑图、集群行为等的物理内在机制.不同的节律可以用具有不同频率的振子(极限环)来刻画,它们之间的同步可以用耦合极限环系统的动力学来加以研究.微观动力学表明,随着耦合强度增强,振子同步伴随着动力学状态空间降维到一个低维子空间,该空间由序参量来描述.序参量的涌现及其所描述的宏观动力学行为可借助于协同学与流形理论等降维思想来进行.本文从统计物理学的角度讨论了耦合振子系统序参量涌现的几种降维方案,并对它们进行了对比分析.序参量理论可有效应用于耦合振子系统的同步自组织与相变现象的分析,通过进一步研究序参量的动力学及其分岔行为,可以对复杂系统的涌现动力学有更为深刻的理解.     

耦合电路系统的分岔研究

研究了由两个非线性电路系统耦合所构成的系统,给出高维系统平衡点的存在性条件和具体解析形式,分析了平衡点的余维1和余维2分岔,并对极限环进行了延拓,得到比较复杂的分岔形式.两个周期运动的子系统在不同的耦合参数下相互作用时,可能导致周期运动、混沌等丰富的动力学行为,通过对耦合前后平衡点的定性分析,得到了在弱耦合情况下平衡点变为中立型鞍点与分岔图出现的不连续现象之间的联系.     

非线性传送带系统的复杂分岔

讨论了一类单自由度非线性传送带系统. 首先通过分段光滑动力系统理论得出系统滑动区域的解析分析和平衡点存在性条件; 其次利用数值方法, 对系统几种类型的周期轨道进行单参数和双参数延拓, 得到系统的余维一滑动分岔曲线和若干余维二滑动分岔点, 以及系统在参数空间中的全局分岔图. 通过对系统分岔行为的研究, 反映出传送带速度和摩擦力振幅对系统动力学行为有较大影响, 揭示了非线性传送带系统的复杂动力学现象. 关键词： 传送带系统 滑动分岔 周期运动     

Nonlinear wave modulations in plasmas

A review of the generic features as well as the exact analytical solutions of coupled scalar field equations governing nonlinear wave modulations in plasmas is presented. Coupled sets of equations like the Zakharov system, the Schrödinger-Boussinesq system and the Schrödinger-KDV system are considered. For stationary solutions, the latter two systems yield a generic system of a pair of coupled, ordinary differential equations with many free parameters. Different classes of exact analytical solutions of the generic system which are valid in different regions of the parameter space are obtained. The generic system is shown to generalize the Hénon-Heiles equations in the field of nonlinear dynamics to include a case when the kinetic energy in the corresponding Hamiltonian is not positive definite. The relevance of the generic system to other equations like the self-dual Yang-Mills equations, the complex KDV equation and the complexified classical dynamical equations is also pointed out.     

The ground state and the tunnelling dynamics of the Bose-Einstein condensate in a tilted shallow trap

The ground state and the tunnelling dynamics of the Bose-Einstein condensate (BEC) loaded in a tilted shallow trap is studied analytically and numerically. The stable bound state, the quasi-bound state and the diffusion state are predicted. The thresholds for transition between the different states are obtained and the stability diagram in parameter space is presented. The tunnelling dynamics of the system in different states is revealed. The shape of the potential well and the atomic interaction play important role and have coupled effect on the tunnelling dynamics of the system. Furthermore, the resonant tunnelling phenomenon in the parametrically modulated shallow trap is observed. The results show that when the modulating frequency approaches the dipolar mode of the system, resonant tunnelling occurs and the whole system is unstable. Our results provide a theoretical evidence for studying the tunnelling dynamics of the ultracold atomic system.     

Nonequilibrium dynamics of ultracold Fermi superfluids

The aim of this mini review is to survey the literature on the study of nonequilibrium dynamics of Fermi superfluids in the BCS and BEC limits, both in the single channel and dual channel cases. The focus is on mean field approaches to the dynamics, with specific attention drawn to the dynamics of the Ginzburg-Landau order parameters of the Fermi and composite Bose fields, as well as on the microscopic dynamics of the quantum degrees of freedom. The two approaches are valid approximations in two different time scales of the ensuing dynamics. The system is presumed to evolve during and/or after a quantum quench in the parameter space. The quench can either be an impulse quench with virtually instantaneous variation, or a periodic variation between two values. The literature for the order parameter dynamics, described by the time-dependent Ginzburg-Landau equations, is reviewed, and the works of the author in this area highlighted. The mixed phase regime in the dual channel case is also considered, and the dual order parameter dynamics of Fermi-Bose mixtures reviewed. Finally, the nonequilibrium dynamics of the microscopic degrees of freedom for the superfluid is reviewed for the self-consistent and non self-consistent cases. The dynamics of the former can be described by the Bogoliubov de-Gennes equations with the equilibrium BCS gap equation continued in time and self -consistently coupled to the BdG dynamics. The latter is a reduced BCS problem and can be mapped onto the dynamics of Ising and Kitaev models. This article reviews the dynamics of both impulse quenches in the Feshbach detuning, as well as periodic quenches in the chemical potential, and highlights the author’s contributions in this area of research.     

Regularities of spectral component behavior near the phase synchronization boundary in spatially extended systems

In this work we study the dynamics of spatially coupled systems using the example of unidirectionally coupled Pierce diodes near the boundary of phase chaotic synchronization. We show that the dynamics in the investigated region of the coupling parameter obeys a universal regularity valid for different space points of the system.     

Dynamics between order and chaos revisited

We show that dynamics between order and chaos, namely strange nonchaotic dynamics can be efficiently studied by means of recurrence properties. Different transitions to this dynamics in coupled R?ssler oscillators are revealed by some measures of complexity based on the recurrence time, which is the time needed for a system to recur to a former visited neighborhood. Furthermore, regions of the parameter space where the system is in non-phase, imperfect-phase or phase synchronization are depicted by means of recurrence based indices such as the generalized autocorrelation function and the correlation of probability of recurrence.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Polymorphic and regular localized activity structures in a two-dimensional two-component reaction-diffusion lattice with complex threshold excitation

Space-time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh-Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures represent novel sorts of spatially temporal patterns which have not been observed before in typical two-component reaction-diffusion type systems. It is demonstrated that there exist two types of regular structures: single and bound states and three types of polymorphic structures: periodic, quasiperiodic and even chaotic ones. The partition of the parameter plane into regions corresponding to the existence of these different types of structures is carried out. High multistability of regular structures is indicated. The interaction of regular structures is investigated. The correspondence between the structures and trajectories in multidimensional phase space associated with the system is given. Bifurcation mechanisms leading to the loss of stability of regular structures as well as to a transition from one type of polymorphic structure to another are indicated. The mechanisms of formation of regular and polymorphic structures are discussed.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space

The dynamics and the transition of spiral waves in the coupled Hindmarsh--Rose (H--R) neurons in two-dimensional space are investigated in the paper. It is found that the spiral wave can be induced and developed in the coupled HR neurons in two-dimensional space, with appropriate initial values and a parameter region given. However, the spiral wave could encounter instability when the intensity of the external current reaches a threshold value of 1.945. The transition of spiral wave is found to be affected by coupling intensity D and bifurcation parameter r. The spiral wave becomes sparse as the coupling intensity increases, while the spiral wave is eliminated and the whole neuronal system becomes homogeneous as the bifurcation parameter increases to a certain threshold value. Then the coupling action of the four sub-adjacent neurons, which is described by coupling coefficient D’, is also considered, and it is found that the spiral wave begins to breakup due to the introduced coupling action from the sub-adjacent neurons (or sites) and together with the coupling action of the nearest-neighbour neurons, which is described by the coupling intensity D.     

Transitions in two sinusoidally coupled Josephson junction rotators

We investigate the dynamics of two sinusoidally coupled Josephson junction rotators to provide a clear knowledge of the behaviors in different regions of the parameter space. The dynamical states are identified, and the transitions among these states are studied. The properties of the current–voltage curves are investigated. Further more, we observed the chaotic states in some regions of parameter space. We conjecture it may caused by the competition of two periodic potentials: one is the external field, another is the interacting of two particles.