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Chaotic motion of the dynamical system under both additive and multiplicative noise excitations 下载免费PDF全文
With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map. 相似文献
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In this paper, the complex dynamical behavior of a fractional-order Lorenz-like system with two quadratic terms is investigated. The existence and uniqueness of solutions for this system are proved, and the stabilities of the equilibrium points are analyzed as one of the system parameters changes. The pitchfork bifurcation is discussed for the first time, and the necessary conditions for the commensurate and incommensurate fractional-order systems to remain in chaos are derived. The largest Lyapunov exponents and phase portraits are given to check the existence of chaos. Finally, the sliding mode control law is provided to make the states of the Lorenz-like system asymptotically stable. Numerical simulation results show that the presented approach can effectively guide chaotic trajectories to the unstable equilibrium points. 相似文献
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Duffing-van der Pol系统的随机分岔 总被引:1,自引:0,他引:1
应用广义胞映射图论方法(GCMD)研究了在谐和激励与随机噪声共同作用下的Duffing-van
der Pol系统的随机分岔现象. 系统参数选择在多个吸引子与混沌鞍共存的范围内.
研究发现, 随着随机激励强度的增大,该系统存在两种分岔现象:
一种为随机吸引子与吸引域边界上的鞍碰撞, 此时随机吸引子突然消失;
另一种为随机吸引子与吸引域内部的鞍碰撞, 此时随机吸引子突然增大. 研究证实,
当随机激励强度达到某一临界值时,
该系统还会发生D-分岔(基于Lyapunov指数符号的改变而定义),
此类分岔点不同于上述基于系统拓扑性质改变所得的分岔点. 相似文献
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研究了一类二阶变系数中立型时滞微分方程的振动性.在前人研究的基础上,通过引入函数r(t),使方程一般化,进而由构造函数法,可以得到方程(1)和(2)是振动的充分条件.结果推广并丰富了已有文献的结论. 相似文献
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A simple method to simultaneously achieve synchronization andanti-synchronization in chaotic systems 下载免费PDF全文
In this paper, a novel adaptive control approach is
presented to simultaneously achieve synchronization and
anti-synchronization in partially linear chaotic systems. Through
appropriately separating state vectors of such systems,
synchronization and anti-synchronization could be simultaneously
realized in different subspaces, which may be strictly proven
theoretically. Simulation results for a Lorenz chaotic system and a
new hyper-chaotic system are provided to illustrate the
effectiveness of the proposed method. Finally, a new secure
communication scheme based on such a synchronization phenomenon of
the hyper-chaotic system is demonstrated. Numerical results show
success in transmitting a periodic signal with high security. 相似文献
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为了研究表面织构对聚四氟乙烯(PTFE)复合材料摩擦磨损性能的影响规律及其作用机理,采用BBD响应面法对试验进行设计与分析,利用LSR-2M往复摩擦试验机测试了复合材料的摩擦学性能,建立了织构参数与摩擦系数和体积磨损率之间的二次回归模型,研究了槽宽、间距和角度参数及其交互作用对复合材料摩擦学性能的影响.结果表明:二次回归模型显著,拟合精度分别为82.9%和83.2%,预测出槽宽323.2μm、间距295.4μm、角度88.7°时摩擦系数存在最小值0.147,槽宽331.1μm、间距307.6μm、角度87.6°时体积磨损率存在最大值8.11×10-5 mm3/(Nm);织构增大了初始摩擦系数和体积磨损率,但有利于储存磨屑,在接触应力作用下磨屑中的纳米粒子与槽底及侧面的粗糙峰形成了机械互锁,提高了磨屑的附着力,促进了转移膜的生成. 相似文献
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基于线性随机系统Khasminskii球面坐标变换, 计算了谐和激励中含有随机相位的Duffing 方程的最大Lyapunov指数. 依据平均最大Lyapunov指数符号的变化, 分析随机相位对非线性系统动力学行为的影响.说明随机相位可以产生混沌亦可抑制混沌, 从而可以作为混沌控制的一种方法. 结合对相图、Poincaré截面、时间历程图的分析, 说明上述方法是有效的.
关键词:
随机相位
混沌控制
最大Lyapunov指数
Poincaré截面 相似文献