HOPF BIFURCATION AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF QUARTIC SYSTEM

摘要

This paper studies a class of quartic system which is more general and realistic than the quartic accompanying system.rnx' = -y + ex + lx~2+ mxy + ny~2, y' = x(1 - Ay)(1 + Cy~2), (*)rnwhere C > 0. Sufficient conditions are obtained for the uniqueness of limit cycle of system (*) and some more in-depth conclusion such as Hopf bifurcation.