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
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.