摘要
A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of sufcient conditions which guarantee the persistent property and global attractivity of the system is obtained. Also, by applying the comparison theorem of diferential equations and Fluctuation Lemma, a set of sufcient conditions which ensure the extinction of the prey species and the global attractivity of predator species is obtained. This result shows that for the Lotka-Volterra type predator-prey system, when the value of prey refuge increases, predator species will be driven to extinction due to the lack of food. Our study shows that the alternative food resource predator species is always permanent, which means that prey refuge has no infuence on the permanence of predator species. However, refuge plays an important role in the persistent property of the prey species: large enough prey refuge could keep the persistent property of the prey species, while small enough refuge could lead to the extinction of prey species. Numerical simulations show the feasibility of the main results.
A nonautonomous ratio-dependent Leslie system incorporating a prey refuge is studied in this paper. By applying the comparison theorem of diferential equations and constructing a suitable Lyapunov function, a set of sufcient conditions which guarantee the persistent property and global attractivity of the system is obtained. Also, by applying the comparison theorem of diferential equations and Fluctuation Lemma, a set of sufcient conditions which ensure the extinction of the prey species and the global attractivity of predator species is obtained. This result shows that for the Lotka-Volterra type predator-prey system, when the value of prey refuge increases, predator species will be driven to extinction due to the lack of food. Our study shows that the alternative food resource predator species is always permanent, which means that prey refuge has no infuence on the permanence of predator species. However, refuge plays an important role in the persistent property of the prey species: large enough prey refuge could keep the persistent property of the prey species, while small enough refuge could lead to the extinction of prey species. Numerical simulations show the feasibility of the main results.
