Abstract
We study a system of ODE'S modelling the interaction of one predator and one prey
This system defines a two-species community which incorporates competition among prey in the absence of any predators as well as a density-dependent predator specific death rate. This system is investigated under ecologically natural regularity conditions and assumptions on g, p and h to ensure the existence and uniqueness of limit cycles. The proof uses the standard Hopf-Andronov bifurcation theory and the technique of Liénard's equation.
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Moreira, H.N. On Liénard's equation and the uniqueness of limit cycles in predator-prey systems. J. Math. Biol. 28, 341–354 (1990). https://doi.org/10.1007/BF00178782
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DOI: https://doi.org/10.1007/BF00178782