Latest News

About CAMQ

Information for Authors

Editorial Board

Browse CAMQ Online

Subscription and Pricing

CAMQ Contacts

CAMQ Home

 

Volume 17,     Number 1,     Spring 2009

 

LIMIT CYCLES OF DIFFERENTIAL SYSTEMS
VIA THE AVERAGING METHODS
DINGHENG PI AND XIANG ZHANG

Abstract. In this article we first recall the averaging methods which are useful in studying limit cycle bifurcations from simple differential systems under small perturbations. We then review some recent results on limit cycle bifurcations obtained by using the averaging methods. Finally we present a new result by applying the averaging method to study the Hopf bifurcation of some smooth differential systems in Rn , we show that the function in the number of limit cycles bifurcated from one singularity of the systems can be an exponential function in the dimension of the system with exponent n - 2, and that the function can also be a power function in the degree of the system with its nonlinear part a polynomial. As we know this last phenomena is first found using the averaging method, which is an extension of Theorem 1 of [29].

 

Download PDF Files
 
(Subscribers Only)

© 2006-2010 Canadian Applied Mathematics Quarterly (CAMQ)