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Bifurcation analysis of a plant-herbivore model with toxin-determined functional response |
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| Authors: | Rongsong Liu Huaiping Zhu |
| Affiliation: | a Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA b Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada c Department of Biology, University of Miami, Coral Gables, FL 33124, USA |
| 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. |
| Keywords: | Plant-herbivore model Stability Limit cycle Homoclinic bifurcation |
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