On a periodic multi-species ecological model

摘要

A periodic predator-prey model with m-predators and n-preys is proposed in this paper, which can be seen as the modification of the traditional Lotka–Volterra model. By using comparison theorem, the ultimately bounded region of the system is obtained. By using comparison theorem and Brouwer fixed point theorem, sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained. Finally, by constructing a suitable Lyapunov function, some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system. The results obtained here generalized the main results of [J.D. Zhao, W.C. Chen, Global asymptotic stability of a periodic ecological model, Applied Mathematics and Computation, 147(3) (2004), 881–892].