The discontinuous planar piecewise linear systems with two improper nodes have at most one limit cycle

被引：0

作者：

Chen, Lu ^{[1
]}

Liu, Changjian ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2024年 / 80卷

关键词：

Discontinuous planar piecewise linear systems; Two improper nodes; Limit cycles; Successor function; Upper bounds; DIFFERENTIAL-SYSTEMS; FILIPPOV SYSTEMS; BIFURCATION;

D O I：

10.1016/j.nonrwa.2024.104180

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence and number of limit cycles of planar piecewise linear systems with two improper nodes are studied. By constructing the Poincar & eacute; half maps and the successor function, we prove that such systems have at most one limit cycle, and when the limit cycle exists, it must be hyperbolic. Furthermore, we explicitly give the parameter regions where the limit cycle exists.

引用

页数：9

共 30 条

[1]

ANDRONOV AA, 1966, THEORY OSCILLATORS

[2] PIECEWISE LINEAR PERTURBATIONS OF A LINEAR CENTER [J].

Buzzi, Claudio ;

Pessoa, Claudio ;

Torregrosa, Joan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (09) :3915-3936

[3] Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region [J].

Carmona, Victoriano ;

Fernandez-Sanchez, Fernando ;

Novaes, Douglas D. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 123

[4] Uniform upper bound for the number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line [J].

Carmona, Victoriano ;

Fernandez-Sanchez, Fernando ;

Novaes, Douglas D. .

APPLIED MATHEMATICS LETTERS, 2023, 137

[5] Integral characterization for Poincare half-maps in planar linear systems [J].

Carmona, Victoriano ;

Fernandez-Sanchez, Fernando .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 305 :319-346

[6] A new simple proof for Lum-Chua's conjecture [J].

Carmona, Victoriano ;

Fernandez-Sanchez, Fernando ;

Novaes, Douglas D. .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2021, 40

[7]

DiBernardo M, 2008, APPL MATH SCI, V163, P1, DOI 10.1007/978-1-84628-708-4

[8] Bifurcation sets of continuous piecewise linear systems with two zones [J].

Freire, E ;

Ponce, E ;

Rodrigo, F ;

Torres, F .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1998, 8 (11) :2073-2097

[9] A general mechanism to generate three limit cycles in planar Filippov systems with two zones [J].

Freire, Emilio ;

Ponce, Enrique ;

Torres, Francisco .

NONLINEAR DYNAMICS, 2014, 78 (01) :251-263

[10] Planar Filippov Systems with Maximal Crossing Set and Piecewise Linear Focus Dynamics [J].

Freire, Emilio ;

Ponce, Enrique ;

Torres, Francisco .

PROGRESS AND CHALLENGES IN DYNAMICAL SYSTEMS, 2013, 54 :221-232

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