scholarly journals Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters

2021 ◽  
Vol 20 (1) ◽  
pp. 55-75
Author(s):  
Meilan Cai ◽  
◽  
Maoan Han ◽  
Keyword(s):  
Limit Cycle ◽  
Piecewise Smooth ◽  
Multiple Parameters ◽  
Cubic Systems

scholarly journals Limit Cycles of a Class of Piecewise Smooth Liénard Systems

2016 ◽  
Vol 26 (01) ◽  
pp. 1650009 ◽  
Author(s):  
Lijuan Sheng
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Function Theory ◽  
Polynomial Systems ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
Piecewise Polynomial ◽  
Multiple Parameters ◽  
Liénard Systems ◽  
Limit Cycle Bifurcation

In this paper, we study the problem of limit cycle bifurcation in two piecewise polynomial systems of Liénard type with multiple parameters. Based on the developed Melnikov function theory, we obtain the maximum number of limit cycles of these two systems.

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Bifurcation of Periodic Orbits Crossing Switching Manifolds Multiple Times in Planar Piecewise Smooth Systems

2019 ◽  
Vol 29 (12) ◽  
pp. 1950160
Author(s):  
Zhihui Fan ◽  
Zhengdong Du
Keyword(s):  
Limit Cycle ◽  
Periodic Orbits ◽  
Limit Cycles ◽  
Sufficient Conditions ◽  
Piecewise Smooth ◽  
Unperturbed System ◽  
Piecewise Smooth Systems ◽  
Smooth Curves ◽  
Switching Curve ◽  
Smooth System

In this paper, we discuss the bifurcation of periodic orbits in planar piecewise smooth systems with discontinuities on finitely many smooth curves intersecting at the origin. We assume that the unperturbed system has either a limit cycle or a periodic annulus such that the limit cycle or each periodic orbit in the periodic annulus crosses every switching curve transversally multiple times. When the unperturbed system has a limit cycle, we give the conditions for its stability and persistence. When the unperturbed system has a periodic annulus, we obtain the expression of the first order Melnikov function and establish sufficient conditions under which limit cycles can bifurcate from the annulus. As an example, we construct a concrete nonlinear planar piecewise smooth system with three zones with 11 limit cycles bifurcated from the periodic annulus.

scholarly journals Uniqueness of Limit Cycles for a Class of Cubic Systems with Two Invariant Straight Lines

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Xiangdong Xie ◽  
Fengde Chen ◽  
Qingyi Zhan
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Uniqueness Of Limit Cycles ◽  
Cubic System ◽  
Straight Lines ◽  
Cubic Systems

A class of cubic systems with two invariant straight linesdx/dt=y(1-x2),  dy/dt=-x+δy+nx2+mxy+ly2+bxy2.is studied. It is obtained that the focal quantities ofO(0,0)are,W0=δ; ifW0=0, thenW1=m(n+l); ifW0=W1=0, thenW2=−nm(b+1); ifW0=W1=W2=0, thenOis a center, and it has been proved that the above mentioned cubic system has at most one limit cycle surrounding weak focalO(0,0). This paper also aims to solve the remaining issues in the work of Zheng and Xie (2009).

Limit cycle bifurcations in piecewise-smooth flows

2007 ◽  
pp. 307-353
Author(s):  
Mario di Bernardo ◽  
Alan R. Champneys ◽  
Christopher J. Budd ◽  
Piotr Kowalczyk
Keyword(s):  
Limit Cycle ◽  
Piecewise Smooth
Sign in / Sign up

Export Citation Format

Share Document