Abstract: By utilizing the comparison theorem and Lyapunov
second method, some sufficient conditions for the permanence and
global attractivity of positive periodic solution for a predator-prey
model with mutual interference m ∈ (0, 1) and delays τi are
obtained. It is the first time that such a model is considered with
delays. The significant is that the results presented are related to the
delays and the mutual interference constant m. Several examples are
illustrated to verify the feasibility of the results by simulation in the
last part.
Abstract: Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.
Abstract: In this paper, a delayed predator-prey system with Hassell-Varley-Holling type functional response is studied. A sufficient criterion for the permanence of the system is presented, and further some sufficient conditions for the global attractivity and exponential stability of the system are established. And an example is to show the feasibility of the results by simulation.