Differential equations with infinite number of limit cycles

Limit cycles of differential equations

with P and Q polynomial and relatively prime, then the situation is substantially simpler, at least with respect to the richness of the asymptotic behaviour of the orbits. The Poincaré-Bendixson theorem implies that a bounded ω-limit set (and hence also a bounded α-limit set) of an orbit has to be either a singularity (also called a zero, an equilibrium, a critical point, or a stationary point)...

Limit Cycles of Planar Quadratic Differential Equations

Since Hilbert posed the problem of systematically counting and locating lhe limit cycle of polynomial systems on the plane in 1900, much ef Tort has been expended in its investigation. A large body of literature chiefly by Chinese and Soviet authors has addressed this question in the context of differential equations whose field is specified by quadratic polynomials, In this paper we consider t...

Limit Cycles of Differential

vol. 37 (2008) No. 1 Book review: LIMIT CYCLES OF DIFFERENTIAL EQUATIONS by Colin Christopher and Chengzhi Li In June 2006 Jaume Llibre and Armengol Gasull organized the Advan ed Course on Limit Cy les and Di erential Equations at the Centre de Re er a Matemàti a in Bar elona. There were three le turers: two by the authors of this book and by Sergey Yakovenko. The book under review ontains the ...

Limit Cycles of the Generalized Polynomial Liénard Differential Equations

We apply the averaging theory of first, second and third order to the class of generalized polynomial Liénard differential equations. Our main result shows that for any n, m ≥ 1 there are differential equations of the form ẍ+f(x)ẋ+g(x) = 0, with f and g polynomials of degree n and m respectively, having at least [(n + m− 1)/2] limit cycles, where [·] denotes the integer part function.

Advanced Course On Limit Cycles of Differential Equations