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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, November 22, 2013 - 04:00 to 05:00

Location:

GLK 115

Event Link:

Local Speaker:

Abstract:

MPAs (Marine Protected Areas) are regions where fishing is

restricted or prohibited. As a fisheries management tool, their purpose is

to protect overharvested species and their habitats.

Assume that the fish population consists of a predator and a prey. One

system of nonlinear ODEs describes the predator-prey interaction in the MPA

where fishing is prohibited. A similar but different system describes the

interaction of predator and prey in the Fishing Grounds where fishing is

allowed. Now assume that both predator and prey can move between MPA and

Fishing Ground, in a way that mimics Fick's albeit in an ODE context. How

does the resulting coupled model, consisting of 4 nonlinear ODEs behave?

In a recent Biomathematics Seminar I discussed some features of such a

model.

Then Jan Medlock (OSU, Department of Biomedical Sciences) asked me what

would happen if the MPA dynamics and Fishing Ground dynamics are described

by the more classical (neutrally stable, but not structurally stable)

Lotka-Volterra predator-prey dynamics. In this seminar I will report on some

progress regarding Jan's question. I will show that the coupling tends to

stabilize the system. In the special case that the prey is immobilized, but

the predator can move, I will outline a proof showing global stability based

on the construction of a Lyapunov function, in conjunction with Lasalle's

invariance principle.

No background on MPAs, Lyapunov functions or Lasalle's invariance principle

is required for this talk. The talk should be accessible to undergraduates

who had some exposure to differential equations.