Persistence analysis of a three-species predation-competition discrete time-delay model with feedback control and nonlinear inhibition in the effects of toxicants

Persistence is an important property of the ecosystem. Since the interference of external factors on the ecosystem is inevitable, a new three-species predation-competition discrete model with time delay and feedback control with the effects of toxicants and nonlinear inhibition terms was proposed. By using the comparison principle of difference equations and calculation techniques related to inequalities, sufficient conditions for the permanence of the system was obtained. The results of previous studies have been promoted. The results show that time delays, feedback control and toxic substances will all affect the persistence of the system. Furthermore, an example was given to verify the feasibility of the theoretical result.