Bifurcation analysis of a plant-herbivore model with toxin-determined functional response

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Abstract

A system of ordinary differential equations is considered which models the plant-herbivore interactions mediated by a toxin-determined functional response. The new functional response is a modification of the traditional Holling Type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically. © 2008 Elsevier Inc. All rights reserved.

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Liu, R., Feng, Z., Zhu, H., & DeAngelis, D. L. (2008). Bifurcation analysis of a plant-herbivore model with toxin-determined functional response. Journal of Differential Equations, 245(2), 442–467. https://doi.org/10.1016/j.jde.2007.10.034

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