共查询到19条相似文献,搜索用时 140 毫秒
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通过数值计算分析Duffing系统在双参数平面上最大Lyapunov指数的分布特性,得到系统在双参数平面上混沌运动、稳定周期运动和各种分岔曲线的参数区域,结合系统单参数分岔图和相图等,讨论参数耦合对系统动力学特性的影响和系统在双参数平面上的分岔与混沌过程。结果显示在双参数平面上由于混沌运动的参数区域被一系列的倍周期分岔曲线环包围,导致系统单参数分岔图出现连续周期泡结构,系统局部分岔特性变得非常复杂;在双参数平面上,经叉式分岔后系统出现倍周期分岔等各种分岔曲线,使得系统经叉式分岔后出现各种吸引子共存现象,利用多初值分叉图和胞映射法对系统经叉式分岔后的全局动力学特性进行详细深入地研究,发现系统参数对各吸引子的稳定性和吸引子吸引域的演变规律有重要影响。 相似文献
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采用集中质量法,建立了齿轮-转子-轴承系统的四自由度的弯扭耦合的非线性振动模型,模型考虑了齿轮副间的时变啮合刚度、齿侧间隙、支承间隙以及综合传递误差等非线性因素;推导出系统的量纲一振动微分方程,采用数值积分方法研究多间隙弯扭耦合齿轮传动的运动随转速、齿侧间隙、支承间隙以及阻尼等参数的分岔特性,同时结合Poincaré截面图,全面系统的分析了转速、啮合阻尼、齿侧间隙以及支承间隙等参数对系统分岔特性的影响。结果发现,在一定的齿侧间隙和啮合阻尼下,随着转速的逐渐增加,系统进入混沌的途径包括激变和拟周期分岔,且随着阻尼系数的增加,系统的分岔和混沌运动被抑制,表现为其混沌区域宽度逐渐降低;在一定的转速和啮合阻尼下,而随着齿侧间隙的逐渐增加,系统会从通过激变进入混沌的途径转变成由倍周期分岔途径进入到混沌,且系统在不同的啮合阻尼下最终锁相为混沌、周期四、周期二和周期一运动;在满足一定的转速和啮合阻尼条件下,随着齿侧间隙的增加,系统可通过倍周期分岔进入并锁定为Naimark-sacker分岔。在满足一定的转速、啮合阻尼和齿侧间隙的条件下,随着支承间隙的增加,系统运动进入狭窄的周期五窗口后锁相为周期一运动,且从系统的控制方程和数值解可以发现支承间隙对系统的运动的影响较弱。 相似文献
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为深入探讨流动的稳定性,本文研究了平面不可压缩的五模流动系统的动力学行为及仿真与控制问题.运用分岔图、Lyapunov指数谱和庞加莱截面图分析了系统通过分岔过渡到混沌所展现的复杂动力学行为.数值模拟揭示出该系统可通过Ruelle-TakensNewhouse途径走向混沌,讨论了系统从规则运动转化到混沌运动所具有的普适特征.设计控制器,并利用延迟反馈控制方案,将系统控制到一周期和二周期. 相似文献
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螺旋锥齿轮间隙非线性系统的分岔与混沌 总被引:4,自引:3,他引:1
建立了含间隙的7自由度螺旋锥齿轮动力学方程,结合分岔图和最大Lyapunov指数曲线研究了分岔的演化过程及系统参数对系统分岔和混沌行为的影响.结果表明,分岔图与最大Lyapunov指数曲线从不同层面反映了系统随参数变化的全局特性,揭示出系统随参数变化在周期n、拟周期和混沌运动间反复演化复杂过程的全景;随参数变化系统经三种途径嵌入混沌:经倍周期分岔,由长周期运动嵌入混沌;经Hopf分岔产生拟周期运动,由"磕碰"运动嵌入混沌;拟周期运动经锁相嵌入混沌;负载的加重、阻尼系数的增大和刚度系数的减小有利于扩大系统的稳定区域,减缓、抑制分岔和混沌. 相似文献
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建立了弧齿锥齿轮传动系统的8自由度间隙非线性动力学模型,考虑了齿轮副的时变啮合刚度、传动误差和啮合间隙.以支承刚度和啮合间隙为分岔参数,计算得到了系统的动力学分岔特性和混沌形态,分析了参数变化时系统响应在周期运动与混沌运动之间的转化过程及啮合间隙变化对系统动态传递误差和传动平稳性的影响.研究结果表明,在支承刚度较小时,系统随支承刚度的变化经倍周期分岔由周期进入混沌,经倍周期或拟周期倒分岔由混沌进入周期.支承刚度较大时,系统随支承刚度的变化经倍周期或者拟周期分岔由周期进入混沌,经拟周期倒分岔由混沌进入周期.随着啮合间隙的变化系统经倍周期分岔由周期进入混沌,经倍周期倒分岔由混沌进入周期. 相似文献
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含间隙多约束碰撞振动系统稳定性分析 总被引:1,自引:0,他引:1
针对一类单自由度含间隙多约束碰撞振动系统,通过在碰撞面处建立系统的Poincaré 映射,推导系统的Jacobi
矩阵,将连续动力系统转换为离散动力系统,并利用Gram-Schmidt 正交化和范式归一化计算得到系统的Lyapunov
指数谱。通过数值模拟,计算系统混沌吸引子与周期吸引子的收敛序列,结合系统相图、单参分岔图及Lyapunov 指数
谱,分析系统周期运动稳定性及各类分岔现象,通过控制系统参数双向变化发现相邻周期运动间存在的周期共存现
象,验证该计算方法的有效性和正确性,研究成果可为后续针对该系统的混沌判断及混沌控制提供理论依据。 相似文献
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摘要: 研究两端一般支承垂直放置的输流管道系统,采用非线性动力学分析方法,研究其在自激、参数激励和外激励联合作用下的非线性动力学特性,分析系统出现混沌运动的参数条件和进入混沌运动的途径。数值仿真结果表明,随着平均流速和质量比的增大,系统响应交替出现周期和混沌运动两种形态。系统进入混沌运动的途径为倍周期分岔,由混沌转化为周期运动的途径为倍周期倒分岔。混沌运动和周期运动出现的参数与流体的平均流速和管道端部的支承/约束刚度有很大关联,随着管道端部约束刚度的增大,系统出现混沌运动的区域减小,说明管道端部的约束刚度有益于抑制混沌运动的发生。 相似文献
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M.-F. Danca 《Dynamical Systems: An International Journal》2010,25(2):189-201
In this article we prove numerically, via computer graphic simulations and specific examples, that switching the control parameter of a dynamical system belonging to a class of dissipative continuous dynamical systems, one can obtain a stable attractor. In this purpose, while a fixed step-size numerical method approximates the solution of the mathematical model, the parameter control is switched every few integration steps, the switching scheme being time periodic. The switch occurs within a considered set of admissible parameter values. Moreover, we show via numerical experiments that the obtained synthesized attractor belongs to the class of all admissible attractors for the considered system and matches to the averaged attractor obtained with the control parameter replaced with the averaged switched parameter values. This switched strategy may force the system to evolve along on a stable attractor whatever the parameter values and introduces a convex structure inside of the attractor set via a bijection between the set of parameter control values and the attractors set. The algorithm besides its utility in systems stabilization, when some desired parameter control cannot be directly accessed, may serve as a model for the dynamics encountered in reality or in experiments, e.g. three species food chain models, electronic circuits, etc. This method, compared, for example, to the OGY algorithm where only small perturbations of parameter control can be issued, allows relatively large parameter perturbations. Also, it does not allow to stabilize an unstable orbit but, using an appropriate parameter switching algorithm, it allows to reach an already existing attractor. The present work extends the results we obtained previously and is applied to Lorenz, Rössler and Chen systems. 相似文献
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This paper is devoted to the study of dynamics of non-autonomous Lorenz systems. These systems are formulated and investigated in the context of non-autonomous dynamical systems. First, we prove that such systems admit a compact global attractor and characterize its structure. Then, we obtain conditions of convergence, under which all solutions of the non-autonomous Lorenz systems approach a point attractor. Third, we derive a criterion for existence of almost periodic, quasi-periodic, periodic, and recurrent motions. Finally, we prove a global averaging principle for non-autonomous Lorenz systems. 相似文献
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The pattern of synchronization of a Lorenz system by a periodic sequence of short pulses has been studied during the variation of a parameter determining the appearance of a chaotic attractor. 相似文献
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振动筛系统的Hopf-Hopf-Flip分岔与混沌演化 总被引:1,自引:0,他引:1
建立了振动筛系统的动力学模型和周期运动的六维Poincaré映射,基于Poincaré映射方法和数值仿真分析了此系统在余维三分岔点附近的动力学行为。研究了其Jacobian矩阵两对复共轭特征值和一负实特征值同时穿越单位圆情况下的Hopf-Hopf-Flip分岔,该系统在此类余维三分岔点附近存在周期运动的Hopf分岔、Flip分岔、环面分岔以及"五角星形"概周期吸引子,揭示了环面倍化以及分形出"五角星形"概周期吸引子并向混沌演化的两种非常规过程,它对于振动筛系统的动力学优化设计提供了理论参考。 相似文献
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We give a renormalization group analysis of a system exhibiting a non-smooth pitchfork bifurcation to a strange non-chaotic attractor. For parameter choices satisfying two specified conditions, self-similar behaviour of the attractor on and near the bifurcation curve can be observed, which corresponds to a periodic orbit of an underlying renormalization operator. We examine the scaling properties for various parameter choices including the so-called pitchfork critical point. Finally, we study the autocorrelation function for the system and show that it is equivalent to that present in symmetric barrier billiards. 相似文献
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Gamal M. Mahmoud M.A. Al-Kashif Shaban A. Aly 《Dynamical Systems: An International Journal》2009,24(1):63-79
We study the dynamics and synchronization properties of a system of complex non-linear equations describing detuned lasers. These equations possess a whole circle of fixed points, while the corresponding real variable equations have only isolated fixed points. We examine the stability of their equilibrium points and determine conditions under which the complex equations have positive, negative or zero Lyapunov exponents and chaotic, quasiperiodic or periodic attractors for a wide range of parameter values. We investigate the synchronization of chaotic solutions of our detuned laser system, using as a drive a similar set of equations and applying the method of global synchronization. We find attractors whose three-dimensional projection is not at all similar to the well-known shape of the (real) Lorenz attractor. Finally, we apply complex periodic driving to the electric field equation and show that the model can exhibit a transition from chaotic to quasiperiodic oscillations. This leads us to the discovery of an exact periodic solution, whose amplitude and frequency depend on the parameters of the system. Since this solution is stable for a wide range of parameter values, it may be used to control the system by entraining it with the applied periodic forcing. 相似文献
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轮齿折断是齿轮主要失效形式之一。以包含单双齿交替啮合、轮齿脱啮和齿背接触等的多状态啮合直齿圆柱齿轮传动系统为研究对象,计算齿根危险截面上的弯曲应力,以齿根许用弯曲应力为边界条件,建立防止轮齿折断的齿根安全条件。基于胞映射方法,用四阶Runge-Kutta法数值计算考察区域内随负载和齿侧间隙变化时系统的吸引盆及其演变过程。判断齿根安全条件下吸引盆中不同运动类型吸引域的安全特性得到系统的安全-吸引盆。借助吸引子、多初值分岔图和最大Lyapunov指数图(TLE)分析安全-吸引盆的侵蚀与分岔机理。研究发现:吸引盆中不同运动类型吸引域在齿根安全条件下的安全特性不同;吸引子的出现和消失直接导致安全-吸引盆的分岔;多初值分岔图中出现周期跳跃和分岔是引发安全-吸引盆分岔的主要原因。研究结果可为直齿轮传动系统安全运行提供参考。 相似文献
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Meucci R Salvadori F Naimee KA Brugioni S Goswami BK Boccaletti S Arecchi FT 《Philosophical transactions. Series A, Mathematical, physical, and engineering sciences》2008,366(1864):475-486
By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime).Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. In a bistable regime, the method relies on the knowledge of the frequency components of the two attractors. Near an interior crisis, the method requires retrieval of the unstable orbit colliding with the chaotic attractor.We also show that a suitable parameter modulation is able to control bistability in the Lorenz system. We observe that, for every given modulation frequency, the chaotic attractor is destroyed under a boundary crisis. The threshold control amplitude depends on the control frequency and the location of the operating point in the bistable regime. Beyond the boundary crisis, the system remains in the steady state even if the control is switched off, demonstrating control of bistability. 相似文献