On the stabilizing effect of cannibalism in stage-structured population models
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Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples
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Department of Mathematics, University of Lecce, via Provinciale Lecce-Arnesano, I-73100 Lecce
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Received:
01 March 2006
Accepted:
29 June 2018
Published:
01 August 2006
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MSC :
92D25, 34C23.
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In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism suppresses these cycles; that is, when cannibalism attack rate is increased so that it passes a critical value, the coexistence steady state changes from being unstable to being stable. Numerical simulations are provided together with the mathematical analysis. Our modelling approach is based on balance arguments and a comparison with some early models which predict that a destabilizing effect of cannibalism is performed. Our results agree with the output of growth simulation for some cannibalistic copepods.
Citation: Bruno Buonomo, Deborah Lacitignola. On the stabilizing effect of cannibalism in stage-structured population models[J]. Mathematical Biosciences and Engineering, 2006, 3(4): 717-731. doi: 10.3934/mbe.2006.3.717
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Abstract
In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism suppresses these cycles; that is, when cannibalism attack rate is increased so that it passes a critical value, the coexistence steady state changes from being unstable to being stable. Numerical simulations are provided together with the mathematical analysis. Our modelling approach is based on balance arguments and a comparison with some early models which predict that a destabilizing effect of cannibalism is performed. Our results agree with the output of growth simulation for some cannibalistic copepods.
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