Abstract
This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin–Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.
Highlights
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Note that impulse control is employed to make the Gilpin–Ayala competition model (GACM) stable globally in [6,7], but this paper involves the impulsive disturbance, which is not limited to impulsive control
Some impulse management measures other than impulsive control sometimes occur in ecological management due to accidents, such as releasing animals, hunting animals harmful to the population, and so on
Summary
Neumann zero boundary value means that the populations do not migrate beyond the biosphere boundary. Note that impulse control is employed to make the GACM stable globally in [6,7], but this paper involves the impulsive disturbance, which is not limited to impulsive control. Impulsive disturbance is considered in this paper, not just impulse control. Some impulse management measures other than impulsive control sometimes occur in ecological management due to accidents, such as releasing animals, hunting animals harmful to the population, and so on. These pulse measures mean that the pulse intensity is not necessarily less than 1 based on system stability
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