On bifurcations and chaos in predator-prey models with delay

DOI10.1016/0960-0779(92)90015-FzbMath0753.92022OpenAlexW2147132615WikidataQ115598967 ScholiaQ115598967MaRDI QIDQ1199891

S. Roy Choudhury

Publication date: 17 January 1993

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0960-0779(92)90015-f

zbMATH Keywords

dissipativitycritical valuepower spectraautocorrelation functionsfractal dimensionssupercritical Hopf bifurcationchaotic regimesgeneral predator-prey modelsinterspecies interactionpredator death rateprey birth ratestability of fixed-pointsVolterra-type distributed delays

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Ecology (92D40) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

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Cites Work

• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Time delay in prey-predator models. II: Bifurcation theory
• Stable oscillations in a predator-prey model with time lag
• Stable oscillations in a predator-prey model with time lag
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