On the explosion of a class of continuous-state nonlinear branching processes

In this paper, we consider a class of generalized continuous-state branching processes obtained by Lamperti type time changes spectrally positive Lévy using different rate functions. When explosion occurs to such process, show that the process converges infinity in finite asymptotically along deterministic curve, and identify speed for function regimes. To prove main theorems, also establish new asymptotic result scale process.