Abstract
In this paper, we build a multispecies predator-prey model with mutual interference and time delays. By means of the comparison theorem, Ascoli theorem and Lebesgue dominated convergence theorem, we establish the sufficient conditions of permanence and investigate the existence of a unique almost periodic solution. By constructing a suitable Lyapunov function, we obtain that the positive almost periodic solution is globally attractive. Finally, we give numerical simulations to indicate the complex dynamical behaviors of this system.
Highlights
1 Introduction In population dynamics, the linkages between predator and prey are usually expressed by different functional response functions, which reflect different dynamical behaviors
We aim to investigate the dynamical properties of almost periodic system (1.2), which can greatly enrich the biological background
We obtain the conditions of permanence, global attractivity and uniqueness of positive almost periodic solutions of the system by using the Ascoli theorem, Lebesgue dominated convergence theorem, Lyapunov functions and comparison theorem
Summary
The linkages between predator and prey are usually expressed by different functional response functions, which reflect different dynamical behaviors. Holling [1] carried out a large number of experiments on predator and prey and got some different functional response functions. The mathematical expression of Holling xi (i = 1, 2) model is as follows [2]: αX2 (X) = β2 + X2. A lot of articles studied the ecosystem with interference factors. Their obtained results showed that the effect of this factor should not be ignored [4,5,6,7]. Wang et al [6] concluded that mutual interference had great effect on the relative properties of predator-prey models
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