Taiwanese Journal of Mathematics · 1999 · 73 citations · 7 references
Natural SciencesEcologyMathematicsDynamical SystemsPopulation EcologyBifurcation TheoryLimit CyclesNonlinear DynamicsPopulation DynamicsPredator-prey InteractionsStability TheoryBifurcationBifurcation AnalysisBifurcation Of Limit CyclesHopf BifurcationMathematical EcologyPredator - Prey DynamicsPredator-prey DynamicsPredator-prey Models
In this paper we study the Hopf bifurcation for the Holling- Tanner model, a well-known predator-prey model in mathematical ecology. We show that for some parameter ranges, the Hopf bifurcation is subcritical and thus the system may have multiple limit cycles.
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Stability and Complexity in Model Ecosystems.
Thomas W. Schoener, R. M. May · Evolution · 1974 · 1.8K citations
The Stability and the Intrinsic Growth Rates of Prey and Predator Populations
James T. Tanner · Ecology · 1975 · 433 citations
Life Sciences, Biology, Ecology +15