Bifurcation Phenomena and Dynamic Behavior of Periodic Solutions in First-Order Non-Autonomous Differential Equations

Abstract

We consider equations of the form
dz/dt= α(t) z^3+ β(t) z^2
Where α and β are polynomial functions of t with a real dependent variable, but z is complex such equations were considered by Lins Neto [7]. Our particular interest is the maximum number of periodic solutions which can bifurcate out of the origin following [1] and[3] , we consider different classes of equations C_11,11 , C_18,1 and C_18,2 of the form (4) and we will calculate the maximum possible multiplicity of the origin using theorem [9]. We use Maple to calculate focal values of, C_18,1 , C_18,2 and C_18,3 .