Effects of environmental fluctuation and time delay on ratio dependent hyperparasitism model

A model of host–parasitoid–hyperparasitoid is considered with ratio dependence between parasitoid and hyperparasitoid. First, the conditions for local stability and increasing host fitness due to the effect of hyperparasitism are deduced. Next, we study the effects of stochastic environmental fluctuations and discrete time delay on the system behavior and calculate the corresponding populations variances. Numerical simulations illustrate that populations densities oscillate randomly around equilibrium points. Also, in contrast to previous literature, the simulations carried out here indicate that populations variances oscillate with the increase of time delay.