Existence of eight positive periodic solutions for a food-limited two-species cooperative patch system with harvesting terms

This paper is concerned with a food-limited two-species cooperative patch system with harvesting terms. By using Mawhin’s coincidence degree theory, this paper establishes a new criterion on the existence of at least eight positive periodic solutions for this system under the assumption of periodicity of the parameters. An example is given to illustrate the effectiveness of the result. The ecological interpretation of the result is also given.

► An existence result is given for eight periodic solutions of a cooperative system.
► Some new techniques are employed to obtain a priori bounds on solutions.
► The ecological interpretation is given for the main mathematical result.