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Effect of time delay on a detritus-based ecosystem. (English) Zbl 1127.92042
Summary: Models of detritus-based ecosystems with delay have received a great deal of attention for the last few decades. This paper deals with the dynamical analysis of a nonlinear model of a detritus-based ecosystem involving detritivores and predators of detritivores. We have obtained criteria for local stability of various equilibrium points and persistence of the model system. Next, we have introduced discrete time delays due to recycling of dead organic matters and gestation of nutrients to the growth equations of various trophic levels. With the delay differential equations model system we have studied the effect of time delays on the stability behaviour. Next, we have obtained an estimate for the length of the time delay to preserve the stability of the model system. Finally, the existence of Hopf-bifurcating small amplitude periodic solutions is derived by considering the time delay as a bifurcation parameter.
MSC:
92D40Ecology
34K20Stability theory of functional-differential equations
34K18Bifurcation theory of functional differential equations