异宿轨道

本文利用Melnikov方法研究了这类系统的异宿轨道分叉、次谐分叉和混沌。

In this paper , Melnikov 's method is used to study the heteroclinic orbit bifurcations , Subharmonic bifurcation and chaos in this system .

二次非线性项和三次非线性项共同存在于方程（1）中，使得用解析方法研究这类系统的难度增大，对应Hamilton系统中的同宿轨道或异宿轨道的解析表达式的求解相当困难。

The quadratic nonlinear term and the cubic nonlinear term that coexist in equation ( 1 ), thus causes difficulty in studying this sort of system through the analytical method and correspondingly makes the solution of analytical expression of homoclinic orbit or heteroclinic orbit in Hamilton system extremely difficult .

Melnikov向量与退化情形下的横截异宿轨道

Melnikov Vectors and Transversal Heteroclinic Orbits in Degenerate Cases

谐和激励与有界噪声作用下具有同宿和异宿轨道的Duffing振子的混沌运动

Influence of harmonic and bounded noise excitations on chaotic motion of Duffing oscillator with homoclinic and heteroclinic orbits

我们利用Melnikov型向量给出了系统在退化情形下的横截异宿轨道存在的充分条件。

The sufficient condition assuring the existence of transversal heteroclinic orbits is given by making use of Melnikov vector .

第四章研究了具有同宿轨道、异宿轨道和三势井的Duffing振子在谐和激励与有界噪声扰动下的混沌运动。

Chapter four investigates the chaotic behaviors of a Duffing oscillator with triple well possessing both homoclinic and heteroclinic orbits subject to harmonic and bounded noise excitations .

Rossler对偶原则指出包含一个双变量化学振荡和一个单变量化学延迟的系统可能会产生混沌现象，为构造具有Silnikov同宿轨道和异宿轨道的系统提供了一种方法。

Rossler dual principle shows that a system may be chaotic , which consists of an ordinary two-variable chemical oscillator and an ordinary single-variable chemical hysteresis system . Furthermore , it provides the systematic way to construct the system having homoclinic and heteroclinic orbit .

相图呈现周期轨道、同宿轨道以及异宿轨道.另外系统还存在分叉现象。

In addition , there exist bifurcation phenomena in the system .

研究一类具有同宿轨道、异宿轨道的相对转动非线性动力系统的混沌运动。

Stability and approximate solution of a relative-rotation nonlinear dynamical system under harmonic excitation ;

混沌是系统中一种复杂的动力特性，与同宿轨道、异宿轨道的存在有关。

Chaos which is related to homoclinic and heteroclinic orbit is a complicated dynamical behavior in a system .

研究一类含有两个参数和有理奇性平面哈密顿系统的同宿与异宿轨道。

The paper is devoted to the studying of the homoclinic and heteroclinic orbits in a class of planar Hamiltonian systems with parameters and rational singularity .

通过对含二次和三次非线性项动力方程的讨论，得到了系统的次谐轨道和异宿轨道等，给出了系统出现混沌的条件。

Some non linear dynamic equations with second and third degree variables are discussed , subharmonic orbits , heteroclinic orbits are obtained , and the conditions for chaos to occur are presented .