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本文用胞映射方法画出了GKDV方程未受扰系统和受扰系统的全局吸引域、r步吸引域。 相似文献
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In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China's futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic. 相似文献
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Bifurcations and chaotic threshold for a nonlinear system with an irrational restoring force 下载免费PDF全文
Nonlinear dynamical systems with an irrational restoring force often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational nonlinearity avoiding the conventional Taylor's expansion to retain the natural characteristics of the system. A series of transformations are proposed to convert the homoclinic orbits of the unperturbed system to the heteroclinic orbits in the new coordinate, which can be transformed back to the analytical expressions of the homoclinic orbits. Melnikov's method is employed to obtain the criteria for chaotic motion, which implies that the existence of homoclinic orbits to chaos arose from the breaking of homoclinic orbits under the perturbation of damping and external forcing. The efficiency of the criteria for chaotic motion obtained in this paper is verified via bifurcation diagrams, Lyapunov exponents, and numerical simulations. It is worthwhile noting that our study is an attempt to make a step toward the solution of the problem proposed by Cao Q J et al. (Cao Q J, Wiercigroch M, Pavlovskaia E E, Thompson J M T and Grebogi C 2008 Phil. Trans. R. Soc. A 366 635). 相似文献
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研究一类N维广义非线性Schrdinger方程的孤子解及其性质,研究非线性参数α变化(α→0及α→∞)时孤子性态的变化规律,同时研究该问题的数值解法,得到了该方程的PR差分格式的收敛性和稳定性条件. 相似文献
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We investigate the Hopf bifurcations of the recently proposed smooth-and-discontinuous (SD) oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter a. The nonlinearity presented in this system characterizes irrationality and piecewise linearity for smooth and discontinuous cases, respectively, which could not meet the requirements of the conventional methods due to the barrier of Taylor expansion. Introducing a series of new kinds of elliptic integrals of the first and second kind to the perturbed oscillator, we obtain the Poincare-Birchoff normal forms of Hopf bifurcations for both smooth and discontinuous regimes. We also demonstrate the criteria for the occurrence of Hopf bifurcations, the stability of periodic solutions bifurcating from the equilibria and the excellent agreement between the theoretical and numerical results. 相似文献
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在非线性科学的应用方面,时间序列分析和处理是一个典型问题。本文以太阳黑子为例,阐述了对混沌背景下的一类非线性时间序列。传统的AR模型的预测值可信度不高,而采用基于混沌吸引子的时间序列预测方法,可获得较好的预测效果。 相似文献
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本文运用数值模拟方法深入研究了Duffing振 窄带随机激励下的稳态响应。第一全面研究了产生跳跃现象的参数区域附近Duffing振子的分岔现象。研究发现,位移、速度的二维联合概率密度函数能全面,地表征系统的运动状态,得到了系统响应的位移、速度的二维联合概率密度的各种分岔模式,因而对该问题有了较全面的认识。同时分析了大量不同参数下系统的响应,发现激励参数系统决定着系统的运动状态,尤其激励强度D的影响 相似文献