On Liénard's equation and the uniqueness of limit cycles in predator-prey systems.
We study a system of ODE's modelling the interaction of one predator and one prey dx/dt = xg(x) - yp(x), dy/dt = gamma y[- delta - nu y - alpha y2 + h(x)]. 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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Departamento de Matemática, Universidade do Amazonas, Manaus-Am, Brazil.
D000818:Animals; D001070:Appetitive Behavior; D004463:Ecology; D008433:Mathematics; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior