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

共 50 条

[31] On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
S. V. Gonchenko
L. P. Shilnikov
D. V. Turaev
Regular and Chaotic Dynamics, 2009, 14
[32] Octonionic Lorenz-like condition
MURAT TANIŞLI
BERNARD JANCEWICZ
Pramana, 2012, 78 : 165 - 174
[33] On discrete Lorenz-like attractors
Gonchenko, Sergey
Gonchenko, Alexander
Kazakov, Alexey
Samylina, Evgeniya
CHAOS, 2021, 31 (02)
[34] LORENZ-LIKE CHAOS IN A PARTIAL-DIFFERENTIAL EQUATION FOR A HEATED FLUID LOOP
YORKE, JA
YORKE, ED
MALLETPARET, J
PHYSICA D, 1987, 24 (1-3): : 279 - 291
[35] On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors
Gonchenko, S. V.
Shilnikov, L. P.
Turaev, D. V.
REGULAR & CHAOTIC DYNAMICS, 2009, 14 (01): : 137 - 147
[36] ON LORENZ-LIKE DYNAMIC SYSTEMS WITH STRENGTHENED NONLINEARITY AND NEW PARAMETERS
Liao, Bo
Tang, Yuan Yan
An, Lu
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2010, 8 (02) : 293 - 311
[37] Transformations that preserve the uniqueness of the differential form for Lorenz-like systems
Lainscsek, Claudia
Mendes, Eduardo M. A. M.
Salgado, Gustavo H. O.
Sejnowski, Terrence J.
CHAOS, 2023, 33 (10)
[38] COMPARISON OF LORENZ-LIKE LASER BEHAVIOR WITH THE LORENZ MODEL
HUBNER, U
KLISCHE, W
ABRAHAM, NB
WEISS, CO
COHERENCE AND QUANTUM OPTICS VI, 1989, : 517 - 520
[39] PERIODS AND ENTROPY FOR LORENZ-LIKE MAPS
ALSEDA, L
LLIBRE, J
MISIUREWICZ, M
TRESSER, C
ANNALES DE L INSTITUT FOURIER, 1989, 39 (04) : 929 - 952
[40] Nonlinear analysis in a Lorenz-like system
Dias, Fabio Scalco
Mello, Luis Fernando
Zhang, Jian-Gang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (05) : 3491 - 3500

← 1 2 3 4 5 →