Limit Cycles for Discontinuous Planar Piecewise Linear Differential Systems Separated by an Algebraic Curve
Jaume Llibre,Xiang Zhang +1 more
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TLDR
This work studies how to change the maximum number of limit cycles of the discontinuous piecewise linear differential systems with only two pieces in function of the degree of the discontinuedness of the algebraic curve between the twolinear differential systems.Abstract:
We study how to change the maximum number of limit cycles of the discontinuous piecewise linear differential systems with only two pieces in function of the degree of the discontinuity of the algeb...read more
Citations
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Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve
TL;DR: In this paper, a higher order Melnikov analysis for piecewise linear perturbations of the linear center is presented, where the maximum number of limit cycles H( n ) of a planar piece-wise linear differential system with two zones separated by the curve y = x n can have, where n is a positive integer.
Journal ArticleDOI
Crossing Limit Cycles of Planar Piecewise Linear Hamiltonian Systems without Equilibrium Points
Rebiha Benterki,Jaume Llibre +1 more
TL;DR: In this article, the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points was studied and it was shown that if these systems are separated by a parabola, they can have at most two crossing limit cycles.
Journal ArticleDOI
Limit cycles appearing from the perturbation of differential systems with multiple switching curves
TL;DR: In this article, an upper bound of the number of limit cycles which bifurcate from the period annulus around the origin under nth degree polynomial perturbations is given.
Journal ArticleDOI
Algebraic Limit Cycles in Piecewise Linear Differential Systems
TL;DR: This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems and presents examples exhibiting two explicit hyperbolicgebraic limit cycl...
Journal ArticleDOI
Crossing limit cycles for piecewise linear differential centers separated by a reducible cubic curve
TL;DR: In this paper, the existence of crossing limit cycles and their distribution for piecewise linear differential systems formed by linear differential centers and separated by a reducible cubic curve, formed either by a circle and a straight line, or by a parabola and astraight line.
References
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
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TL;DR: This SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications.
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Differential equations with discontinuous right-hand sides☆
TL;DR: In this article, the existence results for differential equations with discontinuous right-hand sides with great generality are established and proved for high-order ordinary and partial differential equations for the following problem.
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Piecewise-smooth Dynamical Systems: Theory and Applications
TL;DR: Theoretical theory of non-smooth dynamical systems can be found in this paper, where border-collision in piecewise-linear continuous maps and boundary equilibrium bifurcations in flows are discussed.
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