A study of stochastic lotka-volterra models by path integration methods
Friday seminar by Arvid Naess. NB: Note the time and venue.
From January 2009, the Friday seminars will take place in room 3508. They will start at 14:15.
A generalized Lotka-Volterra (L-V) model for a pair of interacting populations of predators and prey is studied. The model accounts for the prey's interspecies competition and therefore is asymptotically stable, whereas its oscillatory behavior is induced by temporal variations in environmental conditions simulated by those in the prey’s reproduction rate. Two models of the variations are considered, each of them combining randomness with ``hidden'' periodicity. The stationary joint probability density function (PDF) of the number of predators and prey is calculated numerically by the path integration (PI) method based on the use of characteristic functions and the Fast Fourier Transform (FFT). The numerical results match those for the asymptotic case of white-noise variations for which an analytical solution is available. Several examples are studied with calculating important characteristics of oscillations, for example expected rate of upcrossings given level of the predators' number. The calculated PDFs may be of predominantly random nature (unimodal) or of predominantly periodic nature (bimodal). Thus, the PI method has been demonstrated to be a powerful tool for studies of the dynamics of predator-prey pairs. The method captures the random oscillations as observed in nature, taking into account potential periodicity in the environmental conditions.
Professor Arvid Naess; PhD, Dr. techn., FASME
Department of Mathematical Sciences
Norwegian University of Science and Technology
NO-7491 Trondheim, Norway