Bifurcations of limit cycles from infinity for a class of quintic polynomial system

In this work, we use an indirect method to investigate bifurcations of limit cycles at infinity for a class of quintic polynomial system, in which the problem for bifurcations of limit cycles from infinity be transferred into that from the origin. By the computation of singular point values, the conditions of the origin (correspondingly, infinity) to be the highest degree fine focus are derived. Consequently, we construct a quintic system with a small parameter and eight normal parameters, which can bifurcates I to 8 limit cycles from infinity respectively, when let normal parameters be suitable values. The positions of these limit cycles without constructing Poincare cycle fields can be pointed out exactly. (C) 2004 Elsevier SAS. All rights reserved.