Almost periodic dynamics of a delayed three-level food-chain model

This paper is concerned with the dynamics of a three-level food-chain model with time delays. By means of Mawhin's continuation theorem of coincidence degree theory, we investigate the existence of positive almost periodic solutions in a three-level food-chain model with time delays. A set of sufficient conditions for the existence of at least one positive almost periodic solution of the model is obtained. In addition, the global asymptotical stability of the almost periodic solution of the above model is also studied. Finally, two examples and simulations are also given to illustrate the main results in this paper.