On the stable periodic solutions of a delayed two-species model of facultative mutualism

Inspired by a delayed single-species population growth model with so-called hereditary effect, we propose a delayed two-species system modelling “facultative mutualism” in this paper. Easily verifiable sufficient conditions are derived for the existence and globally asymptotic stability of positive periodic solutions of system by employing some analysis techniques and Lyapunov functional. Later, we extend the above results to a more general two-species facultative mutualism system involving multiple delays. Some previous results are extended and improved. Biological interpretations on the main results are also given.