A plankton-nutrient ecosystem with resource recycling: deterministic and stochastic analysis

Abstract

The paper deals with the study of a mathematical model of an open ecosystem consisting of two components: abiotic and biotic. The biotic population feeds over the abiotic population. There is a constant input of abiotic resource (nutrient). The dead biotic populations contribute to the abiotic population by means of decomposition. We study the local stability and oscillation of the deterministic and stochastic model system about the non-trivial equilibrium state. Two types of discrete time delays: delay for gestation to feed the abiotic species and the delay for decomposition of the dead biotic species that contribute to the abiotic population are incorporated. We analyze the delayed deterministic model system for stability about the interior equilibrium state. We have estimated the length of discrete time delay for the stability of the system. Then we have analyzed the oscillation due to Hopf-bifurcation of the model system around the equilibrium state considering time delay as a variable parameter. We have studied the effect of random environment to the model system. We evaluate the intensities of the fluctuation of the two species stochastic system by Fourier transform method. We makenumerical simulation of the deterministic delayed model system for stability and oscillatory behaviour and stochastic delay model for evaluation of the variances and to study their ecological significance for the stability and bifurcation behavior of the system.