International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 65-68, Pages 3703-3716
doi:10.1155/S0161171204406577
Effect of randomly fluctuating environment on autotroph-herbivore model system
Tapan Saha1
and Malay Bandyopadhyay2
1Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Calcutta 700009, India
2Department of Mathematics, Scottish Church College, 1 \& 3 Urquhart Square, Calcutta 700006, India
Abstract
First we deal with a brief introduction of the autotroph-herbivore model system along with deterministic analysis of local stability, bifurcation behavior, and persistence of the populations. The second part consists of the stochastic formulation of the model system to incorporate the effect of environmental fluctuation and then analysis of nonequilibrium fluctuation. Stochastic stability criteria of the model system under the influence of random environmental fluctuation are obtained through the convergence conditions of second-order moments.