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Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances. (English) Zbl 1257.92040
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.

MSC:
92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65C20 Probabilistic models, generic numerical methods in probability and statistics
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