Summary
The classical Volterra equations modelling three species predatorprey interactions are considered with the intention of developing global properties of their solutions. Thirty-four different cases are exhibited. Global asymptotic stability is established for all non-loop cases. Global boundedness is established for all but one kind of loop case, and a condition is exhibited which insures boundedness for that case also. Finally a particular case is shown to have unbounded solutions.
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Krikorian, N. The volterra model for three species predator-prey systems: Boundedness and stability. J. Math. Biology 7, 117–132 (1979). https://doi.org/10.1007/BF00276925
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DOI: https://doi.org/10.1007/BF00276925