外控弱周期电流约束下电极B-Z反应体系中的时间自组织

以经典BZ化学反应体系的三变量Oregonator模型及电极过程动力学为基础,提出了外控弱周期电极电流约束下电极BZ反应体系与体相BZ反应体系相互耦合的动力学模型.在体相处于稳定定态参数条件下,系统地研究了外控弱周期电流约束下电极BZ反应体系中的动力学行为,定量分析了电流慢变流型上的准定态稳定性及有利于出现极限环振荡区域.研究表明,与以前所报道的外控弱周期电位约束情况类似,在外控弱周期电流约束下电极BZ反应体系中的极限环振荡区域亦发生了蜕变,但体系对外控电流约束中的这种持续性之周期扰动的响应表现在两个方面:有利于出现极限环振荡区域的缩变及原非振荡区胁迫振荡的出现.     

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.     

线性与周期扰动对BZ反应动力学行为的影响

实验测定BZ反应在其化学计量系数μ取定值1时,其动力学行为表现为单周期振荡态.理论研究了BZ反应加入线性与周期扰动后,系统动力学行为的变化.结果表明,加入线性扰动时,调节扰动参量可以拓宽系统的不稳定区域,在该区域内系统均呈现单周期振荡态;加入周期扰动时,调节扰动幅度可以使系统的演化模式由单周期振荡态转变为2np倍周期振荡态以及混沌态,系统由倍周期振荡进入混沌.这些理论研究结果也被数值模拟研究所证实.     

二次耦合光力学系统的一类高维可控自持振荡行为

光力学系统通常的耦合是光压耦合, 是光场强度和纳米振子位移的一次耦合, 但在光场很强和振子振幅较大的光力学系统中, 非线性的耦合效应会变得非常明显和重要, 而且其所产生的非线性效应对制造具有特殊功能的光力学器件具有重要意义. 本文在二次耦合模型的基础上研究了光腔和振子之间通过二次耦合作用达到能 量平衡状态时系统所产生的自持振荡现象, 给出了二次耦合光力学系统的一般模型, 并通过数值方法研究了系统的定态行为和远离定态的极限环动力学行为, 标定了系统定态响应的稳定区域到极限环行为的分岔点. 发现在调节输入场参数(改变耦合系数)以及光腔和振子的弛豫系数时, 系统的相空间会出现一些稳定的高维自持振荡极限环. 通过数值分析发现该四维极限环在三维相空间的投影都趋于稳定的三维周期轨道, 并且该极限环轨道会随外部调控参数的改变发生扭动, 出现类似二维李萨如图样的稳定纽结结构. 该现象表明: 通过光场与振子的能量耦合, 利用一定强度的外部驱动可以有效控制振子的定态响应和振动, 可以让微振子锁定在具有一定振幅和频率的自发振动上, 为开发物理器件提供了可靠的光力学控制系统. 关键词： 光力系统 二次耦合 自持振荡 极限环     

邻氨基苯甲酸BZ反应体系中的振荡与混沌：I.SCTR实验研究和非线…

本文研究了ＣＳＴＲ中邻氨基苯甲酸苯甲酸ＢＺ反应体系的振荡行为，总结了非化条件下各反应物浓度和流速变化以及温度变化对体系振荡反应的影响规律；同时还考察了催化条件下的体系振荡行为，发现了Ｍｎ（Ⅱ）催化出现复杂振荡筢应序列，非线性动力学理论分析的结果表明复杂振荡是由体系动力学本质决定的确定性行为，并发现由周期走向混沌的演变过程中存在倍周期分岔（或慢周期分岔）迹象；同时，还通过计算分维，研究反应条件对体系     

线状铜电极在磷酸溶液中电流混沌振荡的同步行为

研究了恒电位下两个铜线电极在磷酸溶液中的电流混沌振荡行为 ,通过恒定不同的电位数值 ,改变单个电极的电流振荡混沌行为 ,研究了不同混沌间的相互作用 .调整线电极间的距离 ,研究了电极间距对电流振荡行为的影响 .实验中两电极的振荡间呈现了复杂的耦合作用 ,耦合后的频率与耦合前电极原有的频率不同 .两电极的混沌电流振荡中呈现出同步、准周期同步和反相同步等现象 .电极距离一定时 ,振荡波形差别很大的两电极的电流容易呈现反相同步和准周期同步 ,波形差别不大时容易产生同步 .强的耦合导致电极间电流振荡的同步 ,电极距离的加大 ,电极间电流振荡难以产生同步 .对耦合作用机制也进行了探讨     

非马尔科夫耗散系统长时演化下的极限环振荡现象

本文研究结构化环境中非马尔科夫耗散系统在长时演化下可能出现的极限环振荡现象. 对于欧姆型谱密度环境中的二能级系统, 由于体系只允许一个束缚态模, 给定初态系统在Bloch空间的长时演化将收敛于一个极限环. 研究揭示了极限环半径与环心位置同环境谱密度函数间的关系. 对于多带光子晶体环境中的二能级系统, 由于其可以存在多个束缚态, 研究展现了系统在长时演化下可能出现的收敛于环面或周期或准周期的振荡行为. 有关环面的特征量与环境谱密度间的量化关系同样得以刻画. 论文随后讨论了两比特系统关联量在局域非马尔科夫耗散环境中长时演化可能出现的特征行为.     

MILO中场不稳定性的非线性发展及混沌行为

 以磁绝缘传输线振荡器中电子运动和辐射场演化方程为基础，分析了场与电子相互作用过程中的不稳定性。这种不稳定性的发展导致场出现极限环振荡和混沌。在软非线性区域，辐射场表现为不连续的极限环振荡；在硬非线性区域，辐射场表现为连续的混沌行为。控制失谐量可加速或抑制这些不稳定态的出现。优化和调节参数可控制器件的运行状态, 获得较高的输出功率。     

单模激光Haken-Lorenz系统的振荡解析解

研究了单模激光Haken-Lorenz系统在Hopf 分歧点处的动力学行为.求出了Haken-Lorenz系统的定态解，采用线性稳定性原理对定态解进行了稳定性分析，获得了本征值方程，进而确定了系统的Hopf 分歧点μc.利用级数法求出了系统在分歧点处的时间周期振荡解的解析表达式.通过计算机对系统分歧点处的动力学行为进行了数值模拟，结果表明，系统在分歧点处存在一个极限环，即时间周期振荡解.与理论分析的解析结果相一致.     

广义BVP电路系统的振荡行为及其非光滑分岔机理

探讨了具有分段线性特性的广义BVP电路系统随参数变化的复杂动力学演化过程. 其非光滑分界面将相空间划分成不同的区域, 分析了各区域中平衡点的稳定性, 得到其相应的简单分岔和Hopf分岔的临界条件. 给出了不同分界面处广义Jacobian矩阵特征值随辅助参数变化的分布情况, 讨论了分界面处系统可能存在的分岔行为, 指出当广义特征值穿越虚轴时可能引起Hopf分岔, 导致系统由周期振荡转变为概周期振荡, 而当出现零特征值时则导致系统的振荡在不同平衡点之间转换. 针对系统的两种典型振荡行为, 结合数值模拟验证了理论分析的结果.     

行波管放大器中的电子混沌现象

用自洽方程模拟了波-粒相互作用过程中的电子混沌行为.结果表明：随着电流的增大，电子在相空间的运动轨道将变得混沌，混沌轨道受失谐量的影响.在时间上，电子混沌比场的极限环和混沌振荡出现要早.与场出现极限环振荡的电流阈值相比,出现电子混沌的电流阈值要小；在场呈极限环状态的“软”非线性区域，电子的混沌轨道占据大部分相空间；而在场混沌的“硬”非线性区域，混沌轨道则弥漫在整个相空间.当电流一定时,电子的混沌运动图样是不变的；在一定的电流范围内， 场的极限环和混沌振荡特征是确定的， 但它们的输出功率是不确定的. 关键词： 行波管放大器 电子混沌 相空间轨道 非线性相互作用     

Coherence resonance and noise-induced synchronization in globally coupled Hodgkin-Huxley neurons

The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is optimized by the noise. The coupling of the network can enhance CR in two different ways. In particular, when the coupling is strong enough, the synchronization of the system is induced and optimized by the noise. This synchronization leads to a high and wide plateau in the local CR curve. A bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron. The local-noise-induced limit cycle can evolve to a refined spatiotemporal order through the dynamical optimization among the autonomous oscillation of an individual neuron, the coupling of the network, and the local noise.     

Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime

The study of optomechanical systems has attracted much attention, most of which are concentrated in the physics in the smallamplitude regime. While in this article, we focus on optomechanics in the extremely-large-amplitude regime and consider both classical and quantum dynamics. Firstly, we study classical dynamics in a membrane-in-the-middle optomechanical system in which a partially reflecting and flexible membrane is suspended inside an optical cavity. We show that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, we study the dynamics of the quantum fluctuations around the classical orbits. By using the logarithmic negativity, we calculate the evolution of the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation. We show that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.     

Investigation of oscillation regimes for a modified Carnot engine: I. Conservative oscillation regimes

The Carnot engine, the model from which the concept of entropy arose, is a parametric generator. A certain modification of the engine has allowed it to be brought into the periodic regime of a stable limit cycle. A formula identical to the expression for the oscillation frequency of a Helmholtz resonator has been derived for the piston oscillation frequency in a quasi-harmonic small-amplitude regime. The shape of the piston oscillations and the form of the phase trajectories are considered in computer simulations for various initial conditions and large amplitudes.     

Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities

A model dynamical system with a great many degrees of freedom is proposed for which the critical condition for the onset of collective oscillations, the evolution of a suitably defined order parameter, and its fluctuations around steady states can be studied analytically. This is a rotator model appropriate for a large population of limit cycle oscillators. It is assumed that the natural frequencies of the oscillators are distributed and that each oscillator interacts with all the others uniformly. An exact self-consistent equation for the stationary amplitude of the collective oscillation is derived and is extended to a dynamical form. This dynamical extension is carried out near the transition point where the characteristic time scales of the order parameter and of the individual oscillators become well separated from each other. The macroscopic evolution equation thus obtained generally involves a fluctuating term whose irregular temporal variation comes from a deterministic torus motion of a subpopulation. The analysis of this equation reveals order parameter behavior qualitatively different from that in thermodynamic phase transitions, especially in that the critical fluctuations in the present system are extremely small.Dedicated to Ilya Prigogine on the occasion of his 70th birthday.     

Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent, i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.     

Time delay induced partial death patterns with conjugate coupling in relay oscillators

We investigate the dynamics of delay-coupled relay oscillators with conjugate (or dissimilar) coupling and find the partial death with the phase-flip transition. This phenomenon is quite general and occurs for the limit cycle as well as chaotic relay oscillators. In the regime of partial death, parts of the system oscillate with large amplitude, while other element stays at rest. Using the Stuart-Landau and Rössler oscillators, we demonstrate that partial amplitude death is a robust dynamical state in coupled oscillators. We also studied the mismatch delay and find different types of dynamical pattern with partial death.     

Investigation of oscillation regimes for a modified Carnot engine: II. The Carnot engine is a parametric generator of self-sustained oscillations

The periodic regime of a stable limit cycle for a modified Carnot engine is realized through an algorithmic slide valve. The power, piston oscillation frequency, and efficiency of the engine have been determined in a quasi-harmonic approximation. The modified engine can operate in the regime of a triangular limit cycle (cycles with any number of angles larger than three are realizable). The developed approach to analyzing the dynamic regimes of a Carnot engine allows one to dispense with the concept of entropy.