Results 21 to 30 of about 29,939 (196)
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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On the Number of Limit cycles for Discontinuous piecewise Linear differential Systems in ℝ2n with Two Zones [PDF]
International Journal of Bifurcation and Chaos, 2013 We study the number of limit cycles of the discontinuous piecewise linear differential systems in ℝ2n with two zones separated by a hyperplane. Our main result shows that at most (8n - 6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter.
J. Llibre, F. Rong
semanticscholar +7 more sources
Discrete and Continuous Dynamical Systems - B, 2021 This paper deals with planar discontinuous piecewise linear differential systems with two zones separated by a vertical straight line x = k. We assume that the left linear differential system (x < k) and the right linear differential system (x > k) share the same equilibrium, which is located at the origin O(0, 0) without loss of generality.
Li, Shimin, Llibre, Jaume
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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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Mathematical Physics, Analysis and Geometry, 2023 We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve y= x with n≥ 2. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of n, proving the extended 16th Hilbert problem ...
Llibre, Jaume, Valls, Claudia
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Bases of exponents with a piecewise linear phase in generalized weighted Lebesgue space
Journal of Inequalities and Applications, 2016 The perturbed system of exponents with a piecewise linear phase, consisting of eigenfunctions of a discontinuous differential operator, is considered in this work.
Tofig Najafov +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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Discontinuous collocation methods and gravitational self-force applications
, 2021 Numerical simulations of extereme mass ratio inspirals, the mostimportant sources for the LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation ...
Barack, Leor +3 more
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Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems [PDF]
, 2015 Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an instantaneous event ...
Bender C. M. +8 more
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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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