Nonlinear dynamics in wurtzite InN diodes under terahertz radiation

We carry out a theoretical study of nonlinear dynamics in terahertz-driven n⁺nn⁺ wurtzite InN diodes by using time-dependent drift diffusion equations. A cooperative nonlinear oscillatory mode appears due to the negative differential mobility effect, which is the unique feature of wurtzite InN aroused by its strong nonparabolicity of the Γ₁ valley. The appearance of different nonlinear oscillatory modes, including periodic and chaotic states, is attributed to the competition between the self-sustained oscillation and the external driving oscillation. The transitions between the periodic and chaotic states are carefully investigated using chaos-detecting methods, such as the bifurcation diagram, the Fourier spectrum and the first return map. The resulting bifurcation diagram displays an interesting and complex transition picture with the driving amplitude as the control parameter.     

太赫兹场和倾斜磁场对超晶格电子动力学特性调控规律研究

微带超晶格在磁场和太赫兹场调控下表现出丰富而复杂的动力学行为, 研究微带电子在外场作用下的输运性质对于太赫兹器件设计与研制具有重要意义. 本文采用准经典的运动方程描述了超晶格微带电子在沿超晶格生长方向(z方向)的THz场和相对于z轴倾斜的磁场共同作用下的非线性动力学特性. 研究表明, 在太赫兹场和倾斜磁场共同作用下, 超晶格微带电子随时间的演化表现出周期和混沌等新奇的运动状态. 采用庞加莱分支图详细研究了微带电子在磁场和太赫兹场调控下的运动规律, 给出了电子运行于周期和混沌运动状态的参数区间. 在电场和磁场作用下, 微带电子将产生布洛赫振荡和回旋振荡, 形成复杂的协同耦合振荡. 太赫兹场与这些协同振荡模式之间的相互作用是导致电子表现出周期态、混沌态以及倍周期分叉等现象的主要原因.     

超混沌Lorenz系统

对Lorenz系统添加一个非线性控制器，使之构成四维超混沌Lorenz系统.利用分岔图、Lyapunov指数谱及相图分析方法，研究了超混沌Lorenz系统的运动规律.数值模拟结果表明：新引入参数处于不同取值范围时，超混沌Lorenz系统可以分别呈现收敛、发散、周期、混沌及超混沌动力学行为. 关键词： Lorenz系统 超混沌 Lyapunov指数 分岔     

用连续法计算五维对流模型的定常解和周期解

利用连续算法(Continuation algorithm)对五维对流非线性动力系统的定常解和周期解进行了数值计算。在参数平面Ri-Re上计算出实分岔点曲线、极限点曲线、Hopf分岔点曲线,绘出了分岔图。在分岔图上的不同区域,存在性质不同的稳定解如定常吸引子、周期吸引子等。分析了定常解、周期解的分岔过程。计算结果很好地说明大气中由基本态到对流态再到波动态最后到湍流态的物理转换过程。 连续算法对研究非线性动力系统的分岔以及耗散结构是很有效的计算方法。     

Characterizing bifurcations and chaos in multiwavelength lasers with intensity-dependent loss and saturable homogeneous gain

We consider the nonlinear dynamics of multiwavelength laser cavities with saturable transmitter and saturating homogeneous gain using a simple and general discrete model. Saturable transmitter is an intensity dependent loss in which the transmittance decreases when the incident optical power increases. We determine the condition under which the saturable transmitter will generate behaviors such as stable steady-state lasing states, periodic lasing states, and chaotic lasing states. Indeed, for sufficiently large power, steady-state operation is first destabilized through a Hopf bifurcation which generates periodic lasing solutions. This is followed by a sequence of period doubling bifurcations to chaotic lasing. The bifurcation structure leading to chaos is characterized by three key methods of dynamical systems: a Feigenbaum series, the calculation of Lyapunov exponents and the computation of the correlation dimension of the system. We found that even single wavelength operation can exhibit complex nonlinear dynamics if the loss element is a saturable transmitter.     

A hyperchaos generated from Lorenz system

This paper presents a four-dimension hyperchaotic Lorenz system, obtained by adding a nonlinear controller to Lorenz chaotic system. The hyperchaotic Lorenz system is studied by bifurcation diagram, Lyapunov exponents spectrum and phase diagram. Numerical simulations show that the new system’s behavior can be convergent, divergent, periodic, chaotic and hyperchaotic when the parameter varies.     

一种非线性动力学系统混沌现象的深入研究

本文在实验教学中引入一种非线性混沌摆系统,通过调节混沌摆的驱动力周期演示了该非线性动力学系统出现混沌现象的过程,从而让学生了解混沌现象的参数敏感性、相图特点、频谱特性等基本特性.为了进一步了解该混沌摆的特性,本文建立了该非线性摆系统的简化动力学方程,在数值上对其进行了研究.基于动力学方程的数值模拟,克服了实验上相关参数定量改变困难、摆动稳定性不易控制、实验时间周期长等问题.在数值模拟中,通过改变不同参数得到了相图、频谱图以及分岔图,比较深入详细地对这种混沌摆的相关特性进行了描述,也有利于学生加深对混沌摆的理解.     

一个新的超混沌系统

基于一个新三维混沌系统,通过引入非线性控制器,构造出一个新的四维超混沌系统,并对该系统的动力学行为进行了研究,包括它的Lyapunov指数谱、分岔图等.分析表明,新的四维系统随着新引入的参数变化呈现周期、复杂周期、混沌及超混沌动力学行为;设计的硬件电路的实验结果也证实了相关结果. 关键词： 超混沌 Lyapunov指数 分岔图 混沌电路     

基于周期性扩频的单相H桥逆变器非线性现象的研究

将周期性扩频技术用于变换器中来抑制其电磁干扰和噪声已经得到了论证并被广泛的应用, 但却忽略了其中的非线性现象. 在分析了周期性扩频技术和单相SPWM-H桥正弦逆变器的精确频闪映射模型的基础上, 研究了采用周期性扩频技术的单相H桥正弦逆变器的分岔和混沌现象, 建立了H桥正弦逆变器扩频后的离散模型, 通过时域图、折叠图、分岔图及李雅亚普诺夫指数谱对其非线性现象进行了分析. 研究表明, 扩频后的H桥正弦逆变器在进入非线性区域后更容易进入混沌区, 并且周期扩频的频率会对系统产生初始分岔点的位置产生影响. 关键词： H桥逆变器 周期性扩频 分岔 混沌     

Experiments on the bifurcation behaviour of a forced nonlinear pendulum

We investigate a mechanical system (forced nonlinear torsion pendulum). The state diagram is given as function of both the external driving frequency and the damping parameter. A bifurcation diagram is measured showing period doubling, chaos and periodic windows. The results are in qualitative agreement with the recent theory.     

Experimental evidence for chaotic behaviour of a parametrically forced pendulum

Experimental evidence is presented for chaotic type nonperiodic motions of a parametrically forced pendulum. A bifurcation diagram is measured directly, showing successive subharmonic bifurcations to ?/4, onset of a periodic motion and the appearance of periodic motions via intermittency. The experimentally determined threshold values of the amplitude of the driving force for the first period doublings and the onset of a periodic motion are found to be in good agreement with the theoretical predictions.     

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     

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.     

Bifurcations in a model of magnetoconvection

Bifurcations from oscillatory solutions are studied in a truncated model of two-dimensional Boussinesq magnetoconvection. The fifth order system of nonlinear differential equations is integrated numerically and in certain parameter regimes there is a bifurcation from symmetrical to asymmetrical oscillations followed by a period-doubling cascade. After the accumulation point there is a semiperiodic cascade leading to chaotic behaviour. Then the semiperiodic cascade is repeated in reverse, followed by a period-halving cascade and a bifurcation back to symmetry. Finally, the branch of oscillatory solutions terminates with a symmetrical heteroclinic orbit that connects two saddle-foci. The interval with aperiodic solutions contains many pairs of narrow windows with asymmetrical or symmetrical periodic solutions, each with its own cascade. This pattern of behaviour is likely to occur when a periodic orbit approaches a symmetrical pair of saddle-foci with eigenvalues that satisfy Shil'nikov's inequality.     

一个简单延迟非线性系统的动力学行为及混沌同步

分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果. 关键词： 延迟非线性系统 电路实验 Hopf分支 混沌     

Chaotic transport and current reversal in deterministic ratchets

We address the problem of the classical deterministic dynamics of a particle in a periodic asymmetric potential of the ratchet type. We take into account the inertial term in order to understand the role of the chaotic dynamics in the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the current reversal as a bifurcation from a chaotic to a periodic regime. Close to this bifurcation, we observed trajectories revealing intermittent chaos and anomalous deterministic diffusion.     

Periodic solutions and flip bifurcation in a linear impulsive system

In this paper, the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically. The existence and the stability of period-one solution are discussed by using a discrete map. The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem. The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters. Moreover, the periodic solutions, the bifurcation diagram, and the chaotic attractor, which show their consistence with the theoretical analyses, are given in an example.     

ADDING ONE BIFURCATION IN A ROTOR SYSTEM WITH CLEARANCES

A mathematical model of a rotor system with clearances is analysed by the application of modern nonlinear dynamic theory. From the bifurcation diagrams, it is discovered that the rotor system alternates between periodic and chaotic motions at a supercritical rotational speed, and after undergoing a chaotic region the periodic number of the motion will increase by one. At the same time, the periodic number is equal correspondingly to the integral multiple of the critical rotational speed. At the subcritical rotational speed, it is discovered that the chaotic bands among successive orders of superharmonic responses return to the period one through a reversed period-doubling bifurcation, as a result of a period-doubling bifurcation. It is shown that the increase of damping may reduce the width of the chaotic bands and the amplitude of the periodic response; the increase of nonlinear degree also leads to the reduction of chaotic bandwidth, but makes the amplitude of the subharmonic response increase. So it is suggested that proper damping and correct material selection by considering the dynamic characteristics of the rotor system may reduce the proportion of faults and enhance the dynamic characteristics when designing the rotor system. The working speed should not be selected at N times its natural frequency and should not be set in the chaotic bands among the successive orders of periodic motion for the same purpose.     

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.