Hopf-Like Bifurcations and Asymptotic Stability in a Class of 3D Piecewise Linear Systems with Applications

被引：11
|
作者：
Cristiano, Rony [1 ]
Tonon, Durval J. [1 ]
Velter, Mariana Q. [1 ]
机构：
[1] Univ Fed Goias, Inst Math & Stat, Ave Esperanca S-N,Campus Samambaia, BR-74690900 Goiania, Go, Brazil
来源：
JOURNAL OF NONLINEAR SCIENCE | 2021年 / 31卷 / 04期
关键词：
Piecewise vector fields; Bifurcations; Crossing limit cycle; Asymptotic stability; BOUNDARY EQUILIBRIUM BIFURCATIONS; LIMIT-CYCLES; DIFFERENTIAL-SYSTEMS;
D O I：
10.1007/s00332-021-09724-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main purpose of this paper is to analyze the Hopf-like bifurcations in 3D piecewise linear systems. Such bifurcations are characterized by the birth of a piecewise smooth limit cycle that bifurcates from a singular point located at the discontinuity manifold. In particular, this paper concerns systems of the form (x) over dot = Ax + b(+/-) which are ubiquitous in control theory. For this class of systems, we show the occurrence of two distinct types of Hopf-like bifurcations, each of which gives rise to a crossing limit cycle (CLC). Conditions on the system parameters for the coexistence of two CLCs and the occurrence of a saddle-node bifurcation of these CLCs are provided. Furthermore, the local asymptotic stability of the pseudo-equilibrium point is analyzed and applications in discontinuous control systems are presented.
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页数：37
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