[Blueboard] Invitation to the MS Thesis Defense of Mr. Hanz Martin C. Cheng

Corazon K. Alvarado calvarado at ateneo.edu
Thu Oct 8 10:56:29 PHT 2015

The Department of Mathematics

School of Science and Engineering

invites you to the MS Thesis Defense of

*Mr. Hanz Martin C. Cheng*

*MS Mathematics*

 *Title:   Study of the Diffusive Lotka Volterra System with Holding Type 2
Functional Response*


1.  Dr. Emmanuel A. Cabral

2.  Dr. Elvira P. De Lara-Tuprio

3.  Dr. Job A. Nable

*Adviser:  *Dr. Roden Jason A. David

*Date:  *October 12, 2015

*Time:*    4:30 pm

*Place:*  SEC-A304


Recently, numerous models regarding population dynamics have been proposed.
Some of the model are on medicine and population growth. In this work, we
will be focusing on competing species, more specifically, predator-prey
dynamics. In particular, we will start by studying the Lotka Volterra
Predator Prey system. After which, we will extend the predatorprey model by
introducing a third species. In particular, we will be looking at a 3
species model that simulaes food chain dynamics. The solutions of these
systems will give us the amount of a certain species present at a specific
time t. By adding a diffusion term, we will also be able to determine how
the population diffuses over space as time passes, thus resulting to the
study of the Diffusive Lotka Volterra Systems. As will be shown, these will
be systems of nonlinear differential equations. It is known that it is
difficult to find analytic solutions to these types of systems. Because of
this, we will use dynamical systems to study the stability of the solutions
to the system. After which, we solve the systems numerically. We will be
use spectral collocation methods to determine the solution of the system.
After which, we take our observations into account and determine some
properties of the solutions of the system. Key Words: Diffusion, Lotka
Volterra, Holling Type 2 functional response, Spectral Collocation Methods
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