Cycles in cannibalistic egg-larval interactions |
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Authors: | Alan Hastings |
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Affiliation: | (1) Division of Environmental Studies and Department of Mathematics, University of California, 95616 Davis, CA, USA |
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Abstract: | A model of a cannibalistic larval-egg interaction such as occurs in Tribolium is developed which leads to a system of nonlinear Volterra integral equations. I determine the local stability properties of the unique equilibrium point of the model. A Hopf bifurcation analysis shows that the model always undergoes a subcritical bifurcation when stability is lost. Numerical solutions confirm the presence of multiple attractors over a range of parameter values. The form of the cycles observed in the numerical solutions is analogous to that observed in laboratory populations of Tribolium. |
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Keywords: | Cannibalism Cycles Hopf bifurcation Volterra integral equations Tribolium |
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