International Journal of Mathematical Analysis Vol. 9, 2015, no. 22, 1083 - 1093 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.412381 Number of Limit Cycles for Homogeneous Polynomial System Hero Waisi Salih 1, 2 , Zainal Abdul Aziz 1, 2 and Faisal Salah 1, 3 1 UTM Centre for Industrial and Applied Mathematics 2 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia 3 Department of Mathematics, Faculty of Science, University of Kordofan, Elobid, Sudan. Copyright © 2014 Hero Waisi Salih, Zainal Abdul Aziz and Faisal Salah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper the bifurcation of limit cycles at infinity for a class of homogeneous polynomial system of degree four is examined. This requires a problem for bifurcation of limit cycles at infinity be converted from the original system to the class of complex autonomous differential system. The evaluation of the conditions from the origin to be a centre and the highest degree fine focus results from the calculation of singular point values. A quartic system is constructed for which it can bifurcate with only one limit cycle at infinity when the normal parameters are constant. Keywords: Infinity; Singular point quantities; Quartic differential system; Centre condition; Bifurcation of limit cycles 1. Introduction In this work, the bifurcation of limit cycles is being referred to particularly to the bifurcation at infinity. The computation of the focal values is one way to examine it. In the case of bifurcation of limit cycles at the origin, a lot of work has been done, most of them have been reported in [6, 11]. For the case at infinity, the study is concerned with the following system of degree 2n + 1, [6]