Periodic dynamics of delayed Lotka–Volterra competition systems with discontinuous harvesting policies via differential inclusions

•A more practical form of harvesting management policy (DHP) has been proposed.•We analyze the periodic dynamics of a class of discontinuous and delayed Lotka–Volterra competition systems.•We present a new method to obtain the existence of positive periodic solutions via differential inclusions.•The global convergence in measure of harvesting solution is discussed.

This paper considers a general class of delayed Lotka–Volterra competition systems where the harvesting policies are modeled by discontinuous functions or by non-Lipschitz functions. By means of differential inclusions theory, cone expansion and compression fixed point theorem of multi-valued maps and nonsmooth analysis theory with generalized Lyapunov approach, a series of useful criteria on existence, uniqueness and global asymptotic stability of the positive periodic solution is established for the delayed Lotka–Volterra competition systems with discontinuous right-hand sides. Moreover, the global convergence in measure of harvesting solution is discussed. Our results improve and extend previous works on periodic dynamics of delayed Lotka–Volterra competition systems with not only continuous or even Lipschitz continuous but also discontinuous harvesting functions. Finally, we give some corollaries and numerical examples to show the applicability and effectiveness of the proposed criteria.