Limit cycles in planar continuous piecewise linear systems
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- 英文论文题名：Limit cycles in planar continuous piecewise linear systems
- 论文作者：ZHANG Ting-ting
- 英文论文作者：ZHANG Ting-ting ; School of Mechanics and Engineering ; Southwest Jiaotong University
- 年：2016
- 作者机构：School of Mechanics and Engineering, Southwest Jiaotong University;
- 英文论文关键词：piecewise linear system ; bifurcation ; limit cycle
- 会议召开时间：2016-05-06
- 会议录名称：第十届动力学与控制学术会议摘要集
- 语种：英文
- 分类号：O19
- 学会代码：AGLU
- 会议名称：第十届动力学与控制学术会议
- 会议地点：中国四川成都
- 主办单位：中国力学学会动力学与控制专业委员会
- 学会名称：中国力学学会
- 页数：2
- 文件大小：908k
- 原文格式：D
- 会议级别：全国
摘要
In this paper an asymmetric planar continuous piecewise linear differential system with three zones ■=y-F(x), ■=-g(x) is considered. When xg(x)>0 for ?x≠0 and y=F(x) is a Z-shaped curve, it owns at most two limit cycles, which exist between a linear Hopf bifurcation surface and a double limit cycle bifurcation surface. Moreover, we prove the conjectures proposed by Ponce et al. in [Int. J. Bifur. Chaos 25(2015) 1530008]. When the uniqueness equilibrium does not lie in the central region, limit cycles of this system have been completely by others. The aim of this paper give a completely study of limit cycles when this system satisfies xg(x)>0 for ?x≠0, y=F(x) is a Z-shaped curve. The global vector field is continuous but nonsmooth. The study of the number of limit cycles is generically a difficult task and numerical techniques are often used. As we all known, piecewise linear systems are able to reproduce most of the dynamical behavior exhibited by general nonlinear systems.Moreover, they are also becoming an important tool in the understanding of a wide range of dynamical phenomena in several areas of physics,engineering and sciences in general. Here, we furtherly study those considered in Ponce et al.(2015) for the limit cycles in piecewise linear system. And this is worth mentioning that we give a positive answer of the conjecture of Ponce et al.(2015).
In this paper an asymmetric planar continuous piecewise linear differential system with three zones ■=y-F(x), ■=-g(x) is considered. When xg(x)>0 for ?x≠0 and y=F(x) is a Z-shaped curve, it owns at most two limit cycles, which exist between a linear Hopf bifurcation surface and a double limit cycle bifurcation surface. Moreover, we prove the conjectures proposed by Ponce et al. in [Int. J. Bifur. Chaos 25(2015) 1530008]. When the uniqueness equilibrium does not lie in the central region, limit cycles of this system have been completely by others. The aim of this paper give a completely study of limit cycles when this system satisfies xg(x)>0 for ?x≠0, y=F(x) is a Z-shaped curve. The global vector field is continuous but nonsmooth. The study of the number of limit cycles is generically a difficult task and numerical techniques are often used. As we all known, piecewise linear systems are able to reproduce most of the dynamical behavior exhibited by general nonlinear systems.Moreover, they are also becoming an important tool in the understanding of a wide range of dynamical phenomena in several areas of physics,engineering and sciences in general. Here, we furtherly study those considered in Ponce et al.(2015) for the limit cycles in piecewise linear system. And this is worth mentioning that we give a positive answer of the conjecture of Ponce et al.(2015).
In this paper an asymmetric planar continuous piecewise linear differential system with three zones ■=y-F(x), ■=-g(x) is considered. When xg(x)>0 for ?x≠0 and y=F(x) is a Z-shaped curve, it owns at most two limit cycles, which exist between a linear Hopf bifurcation surface and a double limit cycle bifurcation surface. Moreover, we prove the conjectures proposed by Ponce et al. in [Int. J. Bifur. Chaos 25(2015) 1530008]. When the uniqueness equilibrium does not lie in the central region, limit cycles of this system have been completely by others. The aim of this paper give a completely study of limit cycles when this system satisfies xg(x)>0 for ?x≠0, y=F(x) is a Z-shaped curve. The global vector field is continuous but nonsmooth. The study of the number of limit cycles is generically a difficult task and numerical techniques are often used. As we all known, piecewise linear systems are able to reproduce most of the dynamical behavior exhibited by general nonlinear systems.Moreover, they are also becoming an important tool in the understanding of a wide range of dynamical phenomena in several areas of physics,engineering and sciences in general. Here, we furtherly study those considered in Ponce et al.(2015) for the limit cycles in piecewise linear system. And this is worth mentioning that we give a positive answer of the conjecture of Ponce et al.(2015).
引文