Abstract
We introduce a generalization of Volterra models with continuous time delay by adding a nonnegative linear vector function of the species. Sufficient conditions for boundedness of solutions and global asymptotic stability of an equilibrium are provided. Applications from population dynamics are presented. One concerns a predator-prey Volterra model with prey-refuges and continuous time delay, and another deals with a Volterra system with currents of immigration for some species. Furthermore, for this kind of model, by a suitable homotopy function, we provide a sufficient condition for the existence of the globally asymptotically stable equilibrium. Finally an example of a simple model in which two predators are competing for one prey which can take shelter is presented.
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