Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

被引：43

作者：

Llibre, Jaume ^{[1
]}

Ponce, Enrique ^{[2
]}

Valls, Claudia ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Escuela Tecn Super Ingn, Dept Matemat Aplicada, Seville 41092, Spain

[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

来源：

JOURNAL OF NONLINEAR SCIENCE | 2015年 / 25卷 / 04期

关键词：

Nonlinear control systems; Periodic orbits; Limit cycles; Lienard piecewise linear differential systems; BIFURCATION SETS; EXISTENCE; NONEXISTENCE; OSCILLATIONS; EQUATIONS;

D O I：

10.1007/s00332-015-9244-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators.

引用

页码：861 / 887

页数：27

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