Global Dynamics Of Asymmetric May-leonard Model

For asymmetric May-Leonard model,dyi/dt=yi(1-yi-βiyi-1-αiyi+1),yi(0)>0,i =1,2,3,y0 = y3,y4 =y1,0<αi<1<βi,i= 1,2,3,I defined θ =(β1-1)(β2-1)(β3-1)-(1-α1)(1-α2)(1-α3).In this thesis,I describe its global dynamics in Poincare ball when θ<0,θ = a,θ>0.