Estimating the number of limit cycles in polynomials systems
نویسندگان
چکیده
منابع مشابه
On the number of limit cycles of the Liénard equation
In this paper, we study a Liénard system of the form ẋ = y−F (x) , ẏ = −x, where F (x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials Rn(x) whose roots of odd multiplicity are related...
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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.
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In this paper we study a general near-Hamiltonian polynomial system on the plane. We suppose the unperturbed system has a family of periodic orbits surrounding a center point and obtain some sufficient conditions to find the cyclicity of the perturbed system at the center or a periodic orbit. In particular, we prove that for almost all polynomial Hamiltonian systems the perturbed systems with p...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.04.024