Bifurcations of a singular prey–predator economic model with time delay and stage structure

Abstract

This paper studies a singular prey–predator economic model with time delay and stage structure. Compared with other researches on dynamics of prey–predator population, this model is described by differential–algebraic equations due to economic factor. For zero economic profit, this model exhibits three bifurcational phenomena: transcritical bifurcation, Hopf bifurcation and singular induced bifurcation. For positive economic profit, the model undergoes a saddle-node bifurcation at critical value of positive economic profit, and the increase of delay destabilizes the positive equilibrium point of the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.