2010, Vol.13, No.3, pp.230-248

The paper deals with the dynamical behavior of a detritus-based ecosystem, mainly found in Sunderban Mangrove area along with deterministic analysis of discrete time delayed local stability due to gestation of the detritus to detritivores in the growth equations of the detritivores and persistence of the population. An estimate on the delay has been carried out by using Nyquist criteria and studied the Hopf-bifurcating small amplitude periodic solution in the neighborhood of the equilibrium points with delay as bifurcation parameter.The second part consists of the stochastic formulation of the model system to incorporate the effect of environmental fluctuation and then analysis of stochastic stability criteria of the model under the influence of random environmental fluctuation.The ecosystem is represented by a set of nonlinear delay differential equations involving detritus, detritivores and predator of detritivores and discuss the robustness of the positive equilibrium with respect to stochastic perturbation.Extensive numerical experiments suggest that a noisy environment for the population is much more destabilizing on the concentration at the equilibrium point than a noisy environment for the population.
Key words: detritus, detritivores, biomathematical modelling, stochastic delay differential equations, persistence, local stability, Hopf-bifurcation, numerical methods for stochastic delay differential equations

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