Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems

Huan, Song-Mei; Yang, Xiao‐Song

doi:10.1016/j.na.2012.07.002

Cited by 21 publications

(5 citation statements)

References 22 publications

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“…These systems exhibit not only standard bifurcations but also complicated dynamical phenomena not existing in smooth systems. The study and classification of various kinds of bifurcation phenomena for piecewise linear systems have attracted great attentions since the last century, see, for example, [4,5] and the references therein. In recent years, many papers studied the bifurcation of limit cycles and the number and distribution of these limit cycles.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Bifurcation of Limit Cycles of a Class of Piecewise Linear Differential Systems in with Three Zones

Cheng

2013

Discrete Dynamics in Nature and Society

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We study the bifurcation of limit cycles from periodic orbits of a four-dimensional system when the perturbation is piecewise linear with two switching boundaries. Our main result shows that when the parameter is sufficiently small at most, six limit cycles can bifurcate from periodic orbits in a class of asymmetric piecewise linear perturbed systems, and, at most, three limit cycles can bifurcate from periodic orbits in another class of asymmetric piecewise linear perturbed systems. Moreover, there are perturbed systems having six limit cycles. The main technique is the averaging method.

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Bifurcation of Limit Cycles of a Class of Piecewise Linear Differential Systems in with Three Zones

Cheng

2013

Discrete Dynamics in Nature and Society

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“…The proof of this family finishes straightforward checking, using ( 16), (17), and (19), that the composition…”

Section: The Center Problemmentioning

confidence: 92%

“…Our computations deal near a focus-focus case. The first stability condition for a general system with an equilibrium point at the origin of focus type and defined in the regions depicted in Figure 1 was done in [19,28]. Previously, but when the discontinuity curve is a straight line, the first terms of the series expansion were obtained also for the fold-fold and fold-focus cases in [10].…”

Section: Introductionmentioning

confidence: 99%

Limit cycles in 4-star-symmetric planar piecewise linear systems

Buzzi¹,

Medrado²,

Torregrosa³

2020

Journal of Differential Equations

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“…In addition to this, as an important common phenomenon the perturbation to discontinuity boundary should also be taken into consideration. In fact, perturbation to discontinuity boundary can result in many new interesting phenomena and affect both the number and type of crossing limit cycles, see [14,25,[47][48][49][50][51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Dynamics in sliding set of planar sector-wise linear systems

Han,

Huan

2023

Phys. Scr.

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For piecewise smooth dynamical systems the existence and properties of some special kinds of sliding points are very important to determine the dynamics (whether local or global), and are also very essential in studying DIBs (i.e., discontinuity induced bifurcations) related to sliding motions. In this paper, we mainly study the inner dynamics of the sliding set of a general planar sector-wise linear differential systems, including the definitions, existence and stability of all special sliding points. Specially, by studying the case when the two zones are separated by straight lines, we obtain explicit dependence on system parameters of the existence, stability and number of all kinds of special sliding points for the planar sector-wise linear systems. Moreover, we provide concrete examples to illustrate our main results and their application in studying DIBs.

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Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems

Cited by 21 publications

References 22 publications

Bifurcation of Limit Cycles of a Class of Piecewise Linear Differential Systems in with Three Zones

Bifurcation of Limit Cycles of a Class of Piecewise Linear Differential Systems in with Three Zones

Limit cycles in 4-star-symmetric planar piecewise linear systems

Dynamics in sliding set of planar sector-wise linear systems

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