Results 21 to 30 of about 24,896 (183)
Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields [PDF]
, 2019 In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields.
Cardoso, Joao L. +3 more
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Limit Cycles for Discontinuous Planar Piecewise Linear Differential Systems Separated by an Algebraic Curve [PDF]
International Journal of Bifurcation and Chaos, 2019 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 algebraic curve between the two linear differential systems. These discontinuous differential systems appear frequently in applied sciences.
Jaume Llibre, Xiang Zhang
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On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system [PDF]
Computational and Applied Mathematics, 2016 Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michel- son differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system.
Llibre, Jaume +2 more
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On the birth of limit cycles for non-smooth dynamical systems [PDF]
, 2014 The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems.
Andronov +31 more
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Regularization of Discontinuous Foliations: Blowing up and Sliding Conditions via Fenichel Theory [PDF]
, 2017 We study the regularization of an oriented 1-foliation $\mathcal{F}$ on $M \setminus \Sigma$ where $M$ is a smooth manifold and $\Sigma \subset M$ is a closed subset, which can be interpreted as the discontinuity locus of $\mathcal{F}$.
da Silva, Paulo Ricardo +1 more
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Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021 Background. The paper proposes a new method for studying differential operators with discontinuous coefficients. We study a sequence of differential operators of high even order whose potentials converge to the Dirac delta function.
S.I. Mitrokhin
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Limit cycles of 3-dimensional discontinuous piecewise differential systems formed by linear centers
São Paulo Journal of Mathematical Sciences, 2021 In this paper we deal with 3-dimensional discontinuous piecewise differential systems formed by linear centers and separated by one plane or two parallel planes. We prove that these systems separated by one plane have no limit cycles, besides the systems separated by two parallel planes have at most one limit cycle, and that there are systems having ...
Jaume LLibre, Jaime R. de Moraes
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Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise [PDF]
, 2013 Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions.
Jeffrey, Mike R., Simpson, David J. W.
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The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems
Nonlinear Dynamics, 2022 In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applications of this kind of differential systems.
Meriem Barkat +2 more
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Advances in Difference Equations, 2019 The Euler scheme is one of the standard schemes to obtain numerical approximations of solutions of stochastic differential equations (SDEs). Its convergence properties are well known in the case of globally Lipschitz continuous coefficients.
S. Göttlich, K. Lux, A. Neuenkirch
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