HOMOCLINIC ORBITS AND THEIR BIFURCATIONS IN DYNAMICAL SYSTEMS WITH TWO DEGREES OF FREEDOM: A METHOD OF QUALITATIVE AND NUMERICAL ANALYSIS

被引：6

作者：

Eleonsky, V. M. ^{[1
]}

Korolev, V. G. ^{[1
]}

Kulagin, N. E. ^{[1
]}

Shil'nikov, L. P. ^{[2
]}

机构：

[1] Lukins Res Inst Phys Problems, Moscow, Zelenograd, Russia

[2] Res Inst Appl Math & Cybernet, Nizjnij Novgorod, Russia

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1993年 / 3卷 / 02期

关键词：

D O I：

10.1142/S0218127493000271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An efficient method of numerical and qualitative analysis of homoclinic trajectories in Hamiltonian systems (or systems possessing a first integral of the motion) with two degrees of freedom is suggested. It allows us to reduce the problem of finding homoclinic loops as intersections of two-dimensional stable and unstable manifolds of an equilibrium point in the four-dimensional phase space to the problem of finding intersections of one-dimensional manifolds (hereafter referred to as touch -curves) on a certain two-dimensional boundary surface. The application of this algorithm in a number of problems leading to Hamiltonian dynamical systems with two degrees of freedom to the analysis of bifurcations of homoclinic loops occurring under the variation of structural parameters, is illustrated.

引用

页码：385 / 397

页数：13

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