二维正弦离散映射的分岔和吸引子

由一个正弦映射和一个三次方映射通过非线性耦合,构成一个新的二维正弦离散映射. 基于此二维正弦离散映射得到系统的不动点以及相应的特征值,分析了系统的稳定性,研究了系统的复杂非线性动力学行为及其吸引子的演变过程. 研究结果表明：此二维正弦离散映射中存在复杂的对称性破缺分岔、Hopf分岔、倍周期分岔和周期振荡快慢效应等非线性物理现象. 进一步根据控制变量变化时系统的分岔图、Lyapunov指数图和相轨迹图分析了系统的分岔模式共存、快慢周期振荡及其吸引子的演变过程,通过数值仿真验证了理论分析的正确性. 关键词： 正弦离散映射 对称性破缺分岔 Hopf分岔 吸引子     

混沌吸引子的对称破缺激变

许多非线性动力系统都有某种对称性,在不同情形下可有不同的表现形式,但始终保持其对称的特点.不同对称形式间的转变导致对称破缺分岔或激变.关于非线性动力系统中相空间运动轨道的对称破缺分岔,已有大量研究工作,但绝大多数是指周期或拟周期相轨的对称破缺,偶尔提到对称系统中的混沌相轨也存在“对偶性”.最近,在简谐外激Duffing系统周期轨道对称破缺引发鞍-结分岔的研究中,得到了分岔后由Poincaré映射点间断流构成的图像,其中包括两个稳定周期结点、一个周期鞍点,及其稳定流形与不稳定流形,均较规则.本工作研究了正弦 关键词： 对称破缺 混沌 激变 分形吸引域     

线性延时反馈Josephson结的Hopf分岔和混沌化

考虑线性延时反馈控制下电阻-电容分路的Josephson结,运用非线性动力学理论分析了受控系统平凡解的稳定性.理论分析表明,随着控制参数的改变,系统的稳定平凡解将会通过Hopf分岔失稳,并推导了发生Hopf分岔的临界参数条件.对不同参数条件下受控系统的动力学进行了数值分析.结果显示,系统由Hopf分岔产生的稳定周期解,将进一步通过对称破缺分岔和倍周期分岔通向混沌. 关键词： 约瑟夫森结 线性延时反馈 Hopf分岔 混沌     

状态反馈和参数调整控制离散非线性系统的倍周期分岔和混沌

利用系统的状态反馈和参数调节的方法，有效地实现了离散非线性动力系统的倍周期分岔的延迟控制和混沌吸引子中不稳定周期轨道的控制.同时，通过选择合适的调控参数，可以将系统从一个2n周期轨道控制到2m(m关键词： 状态反馈 参量调节 混沌控制 分岔控制     

峰值电流模式控制同步开关Z源变换器的动力学研究

Z源变换器由于Z源网络的嵌入,具有高电压传输比,降低开关器件损耗,提高系统效率等优点,在直流变换、逆变等许多领域具有广泛的应用.本文研究了基于峰值电流模式控制的同步开关Z源变换器的非线性动力学,建立了连续电流模式下同步开关Z源变换器的离散迭代映射模型;通过特征值的运动轨迹分析了参考电流对系统稳定性的影响,给出了系统稳定运行的参数域;基于分岔图和Lyapunov指数图发现了此变换器存在倍周期分岔、边界碰撞分岔、切分岔和阵发混沌,分析了边界碰撞分岔和混沌演化过程及其产生的机理;最后通过电路仿真和实验验证了理论分析的正确性.研究结果表明:随着参考电流的增加,峰值电流模式控制同步开关Z源变换器从周期1经历倍周期分岔进入周期2和周期4,然后由于边界碰撞分岔过渡到阵发混沌态,接着通过切分岔进入周期3,最后再次由于边界碰撞分岔进入混沌态.     

logistic模型的倍周期分岔控制

研究了logistic模型的倍周期分岔的控制问题，设计了各种线性控制器，得到了系统在控制前和控制后的分岔图，改变了动力系统的分岔特性.根据实际的应用目的可以设计不同的控制器，使倍周期分岔延迟或提前出现，甚至消失.适当选择控制器增益可以使分岔控制的效果更好. 关键词： logistic模型 倍周期分岔 分岔控制 控制器     

频率扫描法研究倍周期分岔与混沌现象

在一类非线性系统中,应用频率控制方法,对倍周期分岔与混沌行为进行了研究。在V₀-ω外控参数平面上,频率扫描显示了分岔与混沌的整体结构:正的和逆的倍周期分岔序列的对称性;分岔收敛于一点的封闭性。本文中所建议的方法,将是一种研究分岔与混沌现象有效而快速的手段。它不仅能定量测量收敛比δ和标度因子α,分段展开还能定性地观察阵发混沌和嵌套在混沌带中的各种窗口等。分岔与混沌是一类非线性系统的频率响应。 关键词：     

电流模式SEPIC变换器倍周期分岔现象研究

以SEPIC变换器中前置电感电流为控制对象,建立了SEPIC变换器断续电流模式下的离散时间模型, 并分析了不动点的稳定性.通过相轨图、功率谱图以及分岔图, 发现电路中存在一种特殊的倍周期分岔现象——电路的运行状态经历了1倍周期、 2倍周期、4倍周期再到2倍周期、4倍周期,最终进入混沌状态.实验结果与仿真结果相一致, 证实了SEPIC变换器在断续电流模式下存在这种倍周期分岔现象.     

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     

V2控制Buck变换器分岔与混沌行为的机理及镇定

V²控制的Buck变换器在反馈放大系数变化的情况下表现出丰富的非线性行为. 本文建立了V²控制Buck变换器的离散迭代模型, 利用单值矩阵方法研究了系统不稳定行为. 随着反馈放大系数的增大, 变换器从稳定的周期一状态发生一系列的倍周期分岔现象进入周期二、周期四, 不断倍化直至混沌态. 同时其单值矩阵的最大特征值也沿着实负轴穿越单位圆, 从而从稳定性的角度揭示了系统发生一系列倍周期分岔的机理. 基于单值矩阵理论, 利用正弦电压补偿方法镇定了系统的分岔和混沌行为, 得到了镇定后系统的稳定边界. 仿真和实验结果证明了本文分析方法和结论的正确性. 关键词： V²控制')" href="#">V²控制 Buck变换器 分岔 镇定控制     

Insight into Phenomena of Symmetry Breaking Bifurcation

We show that symmetry-breaking (SB) bifurcation is just a transition of different forms of symmetry, while still preserving system's symmetry. SB bifurcation always associates with a periodic saddle-node bifurcation, identifiable by a zero maximum of the top Lyapunov exponent of the system. In addition, we show a significant phase portrait of a newly born periodic saddle and its stable and unstable invariant manifolds, together with their neighbouring flow pattern of Poincaré mapping points just after the periodic saddle-node bifurcation, thus gaining an insight into the mechanism of SB bifurcation.     

Period-doubling/symmetry-breaking mode interactions in iterated maps

We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation equations with Z₂×Z₂ symmetry are derived. A local analysis of solutions is then considered, including the derivation of conditions for a tertiary Hopf bifurcation. Applications to symmetrically coupled maps and to two coupled, vertically forced pendulums are described.     

A normal form for excitable media

We present a normal form for traveling waves in one-dimensional excitable media in the form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behavior of single pulses in a periodic domain and also the richer behavior of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle node in a Bogdanov-Takens point, and a symmetry-breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.     

Critical curves and coexisting attractors in a quasiperiodically forced delayed system

We study three critical curves in a quasiperiodically driven system with time delays, where occurrence of symmetry-breaking and symmetry-recovering phenomena can be observed. Typical dynamical tongues involving strange nonchaotic attractors (SNAs) can be distinguished. A striking phenomenon that can be discovered is multistability and coexisting attractors in some tongues surrounding by critical curves. The blowout bifurcation accompanying with on-off intermittency can also be observed. We show that collision of attractors at a symmetric invariant subspace can lead to the appearance of symmetry-breaking.     

Propagation dynamic of a Gaussian in the inverted nonlinear photonic crystals

In this work, we study the evolution of a Gaussian beam inside a one-dimensional inverted nonlinear photonic crystals (INPC) with a Kerr nonlinearity. The INPC is a kind of virtual crystals which is generated by the optical induction via the electromagnetically induced transparency (EIT). The propagation dynamics of the Gaussian with different total power are identified. Four types of propagation behavior are found. They are collapse beam, breather beam, soliton and symmetry-breaking beam, respectively. The border between these four behavior types are given. For symmetry-breaking beam, an asymmetric profile of the beam is evolving from the symmetry Gaussian, which can be termed as a kind of dynamical symmetry breaking (DSB). The influences on the appearance of the symmetry breaking point are studied by varying input parameters of the Gaussian. The results of this work are both suitable in nonlinear optics and Bose-Einstein condensate (BEC).     

Quantitative calculation and bifurcation analysis of periodic solutions in a driven Josephson junction including interference current

The calculation scheme for periodic solutions in an rf-driven Josephson junction including interference current is derived by using the incremental harmonic balance method. The approximate analytical expressions of stable and unstable periodic orbits are obtained. The stability and bifurcation of the periodic solutions are analyzed based on Floquet theory. The results show that, with the increase of the driving amplitude, one of the periodic solutions undergoes symmetry-breaking and period-doubling bifurcation, which leads to chaos eventually. However, the other periodic solution of the system disappears via a saddle-node bifurcation.     

Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow

New families of three-dimensional nonlinear traveling waves are discovered in pipe flow. In contrast with known waves [H. Faisst and B. Eckhardt, Phys. Rev. Lett. 91, 224502 (2003); H. Wedin and R. R. Kerswell, J. Fluid Mech. 508, 333 (2004), they possess no discrete rotational symmetry and exist at a significantly lower Reynolds numbers (Re). First to appear is a mirror-symmetric traveling wave which is born in a saddle node bifurcation at Re=773. As Re increases, "asymmetric" modes arise through a symmetry-breaking bifurcation. These look to be a minimal coherent unit consisting of one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. Helical and nonhelical rotating waves are also found, emphasizing the richness of phase space even at these very low Reynolds numbers.     

The Oxford Handbook of Philosophy of Physics,edited by R. Batterman

There are three ways in which an expected symmetry may not hold exactly: first, if the basic laws do not respect the symmetry exactly; second, if the initial or boundary conditions do not obey the symmetry; and third, by a spontaneous breakdown, which can happen in two ways, here called SBS1 and SBS2, which will be defined and illustrated. Similar to them is the symmetry-breaking approximation, in which a symmetric system is approximated by an asymmetric formalism to make it easier to handle certain correlations.     

Centrifugal forces alter streamline topology and greatly enhance the rate of heat and mass transfer from neutrally buoyant particles to a shear flow

Centrifugal forces break the degenerate closed-streamline configuration that occurs in simple shear flow past a neutrally buoyant torque-free particle in the inertialess limit. The broken symmetry allows heat or mass to be convected away in an efficient manner in sharp contrast to the inertialess diffusion-limited scenario. The dimensionless transfer rate, characterized by the Nusselt number, is found to be Nu = 0.33(RePe)(1/3) + O(1) for small but finite Re when RePe > 1. Here, the particle Reynolds number (Re) is a dimensionless measure of the inertial forces, while the Peclet number (Pe) measures the relative importance of the convective and the diffusive transfer mechanisms. The symmetry-breaking bifurcation is expected to occur in generic shearing flows, and represents a possible means for heat or mass transfer enhancement from the dispersed phase in multiphase systems.