Periodic sinks and periodic saddle orbits induced by heteroclinic bifurcation in three-dimensional piecewise linear systems with two zones

被引：7

作者：

Wang, Lei ^{[1
]}

Li, Qingdu ^{[2
]}

Yang, Xiao-Song ^{[3
]}

机构：

[1] Hefei Univ, Sch Artificial Intelligence & Big Data, Sino German Inst Appl Math, Hefei 230601, Peoples R China

[2] Univ Shanghai Sci & Technol, Machine Intelligence Inst, Shanghai 200093, Peoples R China

[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 404卷

基金：

中国国家自然科学基金;

关键词：

Periodic orbits; Bifurcation; Stability; Periodic sinks; Periodic saddle orbits; Heteroclinic loops; Piecewise linear systems; GENERALIZED HOPF-BIFURCATION; LIMIT-CYCLE BIFURCATIONS; DIFFERENTIAL-EQUATIONS; HOMOCLINIC LOOP; ODE SYSTEMS; EXISTENCE; DYNAMICS; APPLICABILITY; UNIQUENESS; PROXIMITY;

D O I：

10.1016/j.amc.2021.126200

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For general three-dimensional piecewise linear systems, some explicit sufficient conditions are achieved for the existence of a heteroclinic loop connecting a saddle-focus and a saddle with purely real eigenvalues. Furthermore, certain sufficient conditions are obtained for the existence and number of periodic orbits induced by the heteroclinic bifurcation, through close analysis of the fixed points of the parameterized Poincare map constructed along the hereroclinic loop. It turns out that the number can be zero, one, finite number or countable infinity, as the case may be. Some sufficient conditions are also acquired that guarantee these periodic orbits to be periodic sinks or periodic saddle orbits, respectively, and the main results are illustrated lastly by some examples. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：21

共 45 条

[21] Centennial history of Hilbert's 16th problem
Ilyashenko, Y
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 39 (03): : 301 - 354
[22] Jumps of the fundamental solution matrix in discontinuous systems and applications
Kukucka, Peter
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (11) : 2529 - 2546
[23] Generalized Hopf bifurcation for non-smooth planar systems
Küpper, T
Moritz, S
[J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 359 (1789): : 2483 - 2496
[24] Kuznetsov Y.A., 2013, ELEMENTS APPL BIFURC, V112
[25] One-parameter bifurcations in planar filippov systems
Kuznetsov, YA
Rinaldi, S
Gragnani, A
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (08): : 2157 - 2188
[26] General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
Leonov, G. A.
[J]. PHYSICS LETTERS A, 2012, 376 (45) : 3045 - 3050
[27] Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
Liang, Feng
Han, Maoan
Romanovski, Valery G.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (11) : 4355 - 4374
[28] Existence of piecewise linear differential systems with exactly n limit cycles for all n ∈ N
Llibre, J
Ponce, E
Zhang, X
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 54 (05) : 977 - 994
[29] On the existence and uniqueness of limit cycles in Lienard differential equations allowing discontinuities
Llibre, Jaume
Ponce, Enrique
Torres, Francisco
[J]. NONLINEARITY, 2008, 21 (09) : 2121 - 2142
[30] On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
Llibre, Jaume
Ordonez, Manuel
Ponce, Enrique
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (05) : 2002 - 2012

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