Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems

被引：6

作者：

Leonov, G. A. ^{[1
]}

Mokaev, R. N. ^{[1
,2
]}

Kuznetsov, N., V ^{[1
,2
,3
]}

Mokaev, T. N. ^{[1
]}

机构：

[1] St Petersburg State Univ, Fac Math & Mech, St Petersburg, Russia

[2] Univ Jyvaskyla, Fac Informat Technol, Jyvaskyla, Finland

[3] RAS, Inst Problems Mech Engn, Moscow, Russia

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2020年 / 30卷 / 08期

基金：

俄罗斯科学基金会;

关键词：

Lorenz system; Lorenz-like system; Lorenz attractor; homoclinic orbit; homoclinic bifurcation; strange attractor; LYAPUNOV DIMENSION; STRANGE ATTRACTOR; HIDDEN ATTRACTOR; SHIMIZU-MORIOKA; TRAJECTORIES; EXISTENCE; CASCADE; ORBITS; BIRTH; CHEN;

D O I：

10.1142/S0218127420501242

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic, bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new bifurcation scenarios.

引用

页数：20

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