Persistence, Extinction, and boundedness in pth moment of hybrid stochastic logistic systems by delay feedback control based on discrete-time observation

This paper focuses on the study of long-term behaviour of the stochastic logistic systems under Markov chain using delay feedback control based on discrete-time observations. Necessary conditions for extinction, persistence and boundedness in pth moment of the species in the time average is examined. Particularly, the upper bound of (τ+τ₀) of the time lag between two successive observations τ and the delay time τ₀, is obtained. The stochastic comparison theorem and asymptotic analysis are the main techniques applied. It has been observed that, the delay feedback control has an impact on the persistence of the species. Synthetic examples and virtual realities are given to support the findings.