International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 68, Pages 3703-3716

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

Received 24 June 2004

Copyright © 2004 Tapan Saha and Malay Bandyopadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.