A homotopy technique for a linear generalization of Volterra models (Q1119207)

The author considers a classical n-dimensional Lotka-Volterra model with a constant perturbation term. He finds sufficient conditions that a nonnegative (and non-trivial) equilibrium point which is globally asymptotically stable in a suitable cone exists. His technique is to analyze a homotopy connecting the classical system with the perturbed one and to use an appropriate Lyapunov function. Finally, the results are extended to a Lotka-Volterra system with a retarded perturbation of the form (exponential kernels) which allows translation to a larger system of ordinary differential equations containing auxiliary variables, and to a model of two different Volterra patches connected by discrete diffusion.