On the (1, 3) distributions of limit cycles of plane quadratic systems

Abstract

In this paper, (a) we revise Theorem 2 of Ref. [1] omit the condition\(\bar V_1 > 0\): (b) we discuss the relative positions of six curvesM(s 2, r)=0, J(s2, r)=0, L(s2, r)=0, T(s2, r)=0, s2=s + 2 ands 2=s − 2 . Under the condition of the (1.3) distributions of limit cycles, we expand the variable regions of parameters (s, r) and clearly show them in figure; (c) we study the (1,3) distributions of limit cycles of one kind quadratic systems with two singular points at the infinite; and (d) we give a general method to discuss the (1,3) distibutions of limit cycles of system (1.1) whatever there is one, two or three singular points at the infinite