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On bifurcations and chaos in predator-prey models with delay

✍ Scribed by S.Roy Choudhury

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
945 KB
Volume
2
Category
Article
ISSN
0960-0779

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✦ Synopsis

The stability of the fixed-points of general predator-prey models with Volterra-type distributed delays in the interspecies interaction terms is considered. For general functional forms of prey birth rate and predator death rate and the weak generic kernel or memory function aexp(-at). a supercritical Hopf bifurcation is shown to occur at a critical value au of the parameter a dependent on the system parameters, For four different models, parameter regimes for dissipativity (contraction of phase-space volume) and stable/unstable ranges of a are determined. The four models are integrated numerically, and chaotic regimes are characterized by computing power spectra. autocorrelation functions. and fractal dimensions.

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