Resonance and attenuation in the n-periodic Beverton-Holt equation

An exact expression is derived relating the state average of the periodic solution to the average of the environmental carrying capacities for the periodic Beverton-Holt equation for arbitrary period. By studying numerically period 3 case, we show that the correlation coefficient of the intrinsic growth rates and , is not relevant in determining attenuation or resonance. By studying period 4 case, it is shown that if the intrinsic growth rate jumps upward along with steadily increasing carrying capacities, then resonance prevails. A period 7 example using out-of-step step functions is also seen to produce resonance.