Summary
A Lyapunov function is given that extends functions used by Volterra, Goh, and Hsu to a wide class of predator-prey models, including Leslie type models, and a biological interpretation of this function is given. It yields a simple stability criterion, which is used to examine the effect on stability of intraspecific competition among both prey and predators, of a refuge for the prey, and of Holling type II and type III functional responses. Although local stability analysis of these specific models has been done previously, the Lyapunov function facilitates study of global stability and domains of attraction and provides a unified theory which depends on the general nature of the interactions and not on the specific functions used to model them.
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Harrison, G.W. Global stability of predator-prey interactions. J. Math. Biology 8, 159–171 (1979). https://doi.org/10.1007/BF00279719
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DOI: https://doi.org/10.1007/BF00279719