Event Type:

Mathematical Biology Seminar

Date/Time:

Tuesday, May 14, 2013 - 06:00

Location:

KIDDER 356 (CONFERENCE ROOM)

Event Link:

Local Speaker:

Abstract:

The general class of problems is of the form

dN/dt = g(N(t)), s_i\le t < s_{i+1}, N(s_i) = X_iN(s_i-), i = 1,2,..., N(0) = n_0

where g(0) = 0, s_1 < s_2 < ... are the arrival times of a Poisson renewal process, and X_1,X_2, ... is an i.i.d. sequence of positive random mass fractions, independent of the disturbance times. The state `0' is an absorbing state and therefore the Dirac probability at zero is a trivial invariant distribution. We are interested in obtaining conditions for convergence to a non-trivial steady state. This is accomplished by a combination of Diaconnis-Freedman theory of ``contractions on average'' together with a theory of Lyapounov stability for random systems, neither of which is sufficient on its own. General models from this class were originally introduced to analyze the recovery of populations subject to large random disturbances, e.g., fire, insect infestation, etc. A controlled experiment is being conducted in the Oregon Climate Change Research Institute by an undergraduate Honors College Student Conner Olsen, directed by Heather Lintz, CEOAS, involving episodic disturbances to an algae culture to which a model of this type is being applied. The mathematical development is a collaboration with Scott Peckham, University of Colorado, Boulder.