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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Hastings, A. Cycles in cannibalistic egg-larval interactions. J. Math. Biology 24, 651–666 (1987). https://doi.org/10.1007/BF00275508
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DOI: https://doi.org/10.1007/BF00275508