Summary
It is proved that sufficient conditions for global stability in a Lotka-Volterra model of a two species interactions are (i) the equilibrium is feasible, (ii) the equilibrium is locally stable and (iii) at the equilibrium each species sustains density dependent mortalities due to intraspecific interactions.
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References
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Goh, B.S. Global stability in two species interactions. J. Math. Biol. 3, 313–318 (1976). https://doi.org/10.1007/BF00275063
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DOI: https://doi.org/10.1007/BF00275063