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51.
The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant 下载免费PDF全文
In this paper, the extended Pad'e approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter varepsilon is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values. 相似文献
52.
A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators 下载免费PDF全文
An intrinsic extension of Pad′e approximation method, called the generalized Pad′e approximation method, is proposed based on the classic Pad′e approximation theorem. According to the proposed method, the numerator and denominator of Pad′e approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Pad′e approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Pad′e approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Pad′e approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method. 相似文献
53.
Abstract. In this paper,the Lauwerier map 相似文献
54.
Boling GUO Hanlin CHEN Institute of Applied Physics Computational Mathematics Beijing China Mianyang Normal College Mianyang China 《Communications in Nonlinear Science & Numerical Simulation》2001,(4)
IntroductionIn recent years, there have been extensive studies on the existence of homoclinic orbit5 fOrnear integrable Hamiltonbo partial fferential equations, which are closely related to chaosI1--7].In this work, we consider a perturbed quintic-cubic nonlinear Schr5dinger (NLS) equationwhere q is 27-Periodic and even in x, D is a bounded dissipative operator and is assumed totake the formDq = --aq + jBqfor posititre constants cr and J. Here B is a Fourier truncation of the differentia… 相似文献
55.
Multipulse feed strategy for glycerol fed-batch fermentation 总被引:4,自引:0,他引:4
Dongming Xie Dehua Liu Haoli Zhu Tianzhong Liu 《Applied biochemistry and biotechnology》2001,95(2):103-112
During glycerol fed-batch fermentation, the process could be divided into multiple equal subintervals, and the feed operation
was performed in pulse form at the start of each subinterval. Based on the macrokinetic models, the multipulse feed strategy
for both glucose and corn steep slurry was determined by a general nonlinear optimization approach to maximize the final glycerol
productivity and still control the residual glucose at a low concentration. The experimental results in a 600-mL Airlift Loop
Reactor showed that the tested data with this strategy agreed well with the corresponding model prediction, and that the feed
mode with nonlinear optimization could improve the glycerol productivity significantly compared with those determined just
by limited experimental optimization in previous studies. 相似文献
56.
In this work we study the existence of Silnikov homoclinicorbits in the averaged equations representing the modal interactionsbetween two modes with zero-to-one internal resonance. The fast mode isparametrically excited near its resonance frequency by a periodicforcing. The slow mode is coupled to the fast mode when the amplitude ofthe fast mode reaches a critical value so that the equilibrium of theslow mode loses stability. Using the analytical solutions of anunperturbed integrable Hamiltonian system, we evaluate a generalizedMelnikov function which measures the separation of the stable and theunstable manifolds of an annulus containing the resonance band of thefast mode. This Melnikov function is used together with the informationof the resonances of the fast mode to predict the region of physicalparameters for the existence of Silnikov homoclinic orbits. 相似文献
57.
The solitary wave and wave front are two
important behaviors of nonlinear evolution equations.
Geometrically, solitary wave and wave front are all plane curve.
In this paper, they can be represented in terms of curvature
c(s), which varies with arc length s. For solitary wave when
s → ±∞, then its curvature c(s) approaches
zero, and when s=0, the curvature c(s) reaches its maximum.
For wave front, when s → ±∞, then its
curvature c(s) approaches zero, and when s=0, the curvature
c(s) is still zero, but c'(s) ≠ 0. That is, s=0 is a
turning point. When c(s) is given, the variance at some point
(x,y) in stream line with arc length s satisfies a 2-order
linear variable-coefficient ordinary differential equation. From
this equation, it can be determined qualitatively whether the
given curvature is a solitary wave or wave front. 相似文献
58.
研究一类在参数和强迫激励下发生共振时的两个自由度系统,利用多重尺度法证明存在锁频于Ω的周期解.在一定条件下可变换成Wiggins的系统,给出了判断这类系统同宿轨道存在的计算公式. 相似文献
59.
Cao Yongluo 《数学学报(英文版)》1997,13(1):90-96
In this paper, we consider the families of nearby singular diffeomorphism and the measure of a set in the parameter space,
such that for each point of the set the corresponding diffeomorphism possesses strange attractor. For some families of one-dimensional
mapping satisfying certain transversality condition, we prove that there is a positive measure set in the parameter space,
such that the system in the corresponding families of nearly singular diffeomorphism has strange attractor. Furthermore, we
study the dynamics of this type of strange attractor.
Project Supported by Fund of National Science of China 相似文献
60.
We study bifurcations of periodic orbits in two parameter general unfoldings of a certain type homoclinic tangency (called
a generalized homoclinic tangency) to a saddle fixed point. We apply the rescaling technique to first return (Poincaré) maps
and show that the rescaled maps can be brought to so-called generalized Hénon maps which have non-degenerate bifurcations
of fixed points including those with multipliers e
±iϕ
. On the basis of this, we prove the existence of infinite cascades of periodic sinks and periodic stable invariant circles.
相似文献