publication . Article . Other literature type . 2001

Parametric analysis of the ratio-dependent predator–prey model

Berezovskaya, F.; Karev, G.; Arditi, R.;
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  • Published: 01 Sep 2001 Journal: Journal of Mathematical Biology, volume 43, pages 221-246 (issn: 0303-6812, eissn: 1432-1416, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
We present a complete parametric analysis of stability properties and dynamic regimes of an ODE model in which the functional response is a function of the ratio of prey and predator abundances. We show the existence of eight qualitatively different types of system behaviors realized for various parameter values. In particular, there exist areas of coexistence (which may be steady or oscillating), areas in which both populations become extinct, and areas of “conditional coexistence” depending on the initial values. One of the main mathematical features of ratio-dependent models, distinguishing this class from other predator–prey models, is that the Origin is a c...
Subjects
arXiv: Quantitative Biology::Populations and Evolution
free text keywords: Statistical physics, Qualitative theory, Oscillation, Equilibrium point, Parametric analysis, Control theory, Predation, Mathematical analysis, Extinction, Mathematics, Social ecological model, Ode
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publication . Article . Other literature type . 2001

Parametric analysis of the ratio-dependent predator–prey model

Berezovskaya, F.; Karev, G.; Arditi, R.;