Summary: On the basis of the theories and methods of ecology and ordinary differential equations, a three-species ecological model with allochthonous nutrient input, impulse perturbations and seasonal disturbances is studied analytically and numerically. Using mathematical theoretical analysis, we obtain the threshold expression of the release amount, allochthonous nutrient input and seasonal disturbances parameter under the condition of some species extinction and all species persistence, which in turn provide a theoretical basis for the numerical simulation.
Numerical analysis indicates that the key factors for long-term dynamical behavior are impulse perturbation and allochthonous nutrient input with seasonal disturbances. Nonetheless, it should be stressed that the allochthonous nutrient input with seasonal disturbances can aggravate periodic oscillations and promote the emergence of chaos.These results show that impulse perturbations cannot prevent the indirect effect on complex population dynamics caused by allochthonous nutrient input with seasonal disturbances, which further confirm that allochthonous nutrient input with seasonal disturbances can play an important role in population persistence and evolutionary. All these results are expected to be useful in the study of complex dynamics of ecosystems.