In this paper, a one-prey-n-predator impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated. On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Examples and numerical simulations are presented to verify the feasibility of our results. A discussion is conducted at the end.
ARTICLE HISTORY
Let G : Ω → Ω be a closed unital map between commutative, unital quantales. G induces a functor G from the category of Ω-categories to that of Ω -categories. This paper is concerned with some basic properties of G. The main results are: (1) when Ω, Ω are integral, G : Ω → Ω and F : Ω → Ω are closed unital maps, F is a left adjoint of G if and only if F is a left adjoint of G; (2) G is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for G to preserve completeness in the sense that GA is a complete Ω -category whenever A is a complete Ω-category.
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