Stocking effects on a fish population growth with time lag regulation

The simple logistic model with time lag control is employed to consider the constant rate stocking effects. Stocking increases the equilibrium level of the population. The stability of the equilibrium depends on all parameters employed in the model. The equilibrium becomes unstable and the limit cycle arises under the sufficient level of stocking although the product of the increasing rate and time lag is less than π/2. Stocking produces the increase of the amplitude and the decrease of the period of the population's fluctuation. Careful stocking is desired in controlling natural populations.