Mathematics and Statistics

PhD Defense: Dynamics of Plant-Herbivore Interaction with Chemical Defense and Spatial Diffusions

Author: UNB

Posted on Jan 5, 2014

Category: Seminars and Colloquia

Doctor of Philosophy Thesis Defense
Dynamics of Plant-Herbivore Interaction with Chemical Defense and Spatial Diffusions

Fang Yu (UNB)
Tuesday, January 7, 2014 at 10:00 am
Harriet Irving Library Seminar Room (4th floor)

The purpose of this dissertation is to investigate the dynamics of plant-herbivore interactions with plant defense by assuming the numerical response is not necessarily proportional to the functional response.

We first introduce basic background on plant chemical defense and concepts of functional response and numerical response, then consider a two dimensional system of autonomous differential equations, which models interaction between plant and herbivore. The existence, uniqueness and boundedness of the non-negative solution are proved. Local and global stability of equilibria, Hopf bifurcation, existence of limit cycle are addressed in Chapter 2.

In Chapter 3, a diffusive plant-herbivore system with Neumann boundary conditions is derived. Local and global stability of spatially homogeneous steady states are established. We derive the conditions for the occurrence of Hopf bifurcation and steady state bifurcation and provide geometrical methods to locate the bifurcation values. A large variety of different types of short-term behavior, including oscillations both in space and in time, or oscillations with different amplitudes, are observed.

In Chapter 4, we consider a diffusive plant-herbivore model subject to homogeneous and non-homogeneous Dirichlet boundary conditions. Stability of spatially homogeneous steady states is obtained. Through numerical simulations, we observe several types of transient spatio-temporal behavior including oscillations both in space and in time, or in one of them.

In Chapter 5, a system of two ordinary differential equations is proposed. The system models chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response. This numerical response accounts for the reduction in the herbivore's growth and reproduction due to chemical defenses from plants. It is shown that the system exhibits very rich dynamics including multitype saddle-node bifurcations, Hopf bifurcation, homoclinic bifurcation and multitype bi-stability. Limit cycles, homoclinic orbits and heteroclinic orbits are numerically observed.

In Chapter 6, we discuss our main results and some possible future works.

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Fang Yu is a graduate student of the Mathematics/Statistics GAU
This talk is presented in partial fulfillment of the requirements for the degree