On the Number of Limit Cycles in Piecewise-Linear Liénard Systems
نویسنده
چکیده
In a previous paper [Tonnelier, 2002] we conjectured that a Liénard system of the form ẋ = p(x) − y, ẏ = x where p is piecewise linear on n + 1 intervals has up to 2n limit cycles. We construct here a general class of functions p satisfying this conjecture. Limit cycles are obtained from the bifurcation of the linear center.
منابع مشابه
The number of medium amplitude limit cycles of some generalized Liénard systems
We will consider two special families of polynomial perturbations of the linear center. For the resulting perturbed systems, which are generalized Liénard systems, we provide the exact upper bound for the number of limit cycles that bifurcate from the periodic orbits of the linear center.
متن کاملThe McKean's Caricature of the Fitzhugh--Nagumo Model I. The Space-Clamped System
Within the context of Liénard equations, we present the FitzHugh–Nagumo model with an idealized nonlinearity. We give an analytical expression (i) for the transient regime corresponding to the emission of a finite number of action potentials (or spikes), and (ii) for the asymptotic regime corresponding to the existence of a limit cycle. We carry out a global analysis to study periodic solutions...
متن کاملMaximum Number of Limit Cycles for Certain Piecewise Linear Dynamical Systems
In this paper we compute the maximum number of limit cycles of some classes of planar discontinuous piecewise linear differential systems defined in two half–planes separated by a straight line Σ. Here we only consider non–sliding limit cycles, i.e. the limit cycle does not contain any sliding segment. Among all the cases that we study, in particular, we prove that this maximum number of limit ...
متن کاملOn the Number of Limit cycles for a Generalization of LiéNard Polynomial differential Systems
where g1(x) = εg11(x)+ε g12(x)+ε g13(x), g2(x) = εg21(x) + ε g22(x) + ε g23(x) and f(x) = εf1(x) + εf2(x) + ε f3(x) where g1i, g2i, f2i have degree k, m and n respectively for each i = 1, 2, 3, and ε is a small parameter. Note that when g1(x) = 0 we obtain the generalized Liénard polynomial differential systems. We provide an upper bound of the maximum number of limit cycles that the previous d...
متن کاملMedium Amplitude Limit Cycles of Some Classes of Generalized Liénard Systems
The bifurcation of limit cycles by perturbing a planar system which has a continuous family of cycles, i.e. periodic orbits, has been an intensively studied phenomenon; see for instance [13, 16, 2] and references therein. The simplest planar system having a continuous family of cycles is the linear center, and a special family of its perturbations is given by the generalized polynomial Liénard ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 15 شماره
صفحات -
تاریخ انتشار 2005