Effect of additive and multiplicative noise on the first bifurcations of the logistic model

Abstract

The statistical dynamics of the response of the logistic map, ${x}_{n+1}$=${\mathrm{rx}}_{n}$(1-${x}_{n}$), towards additively and multiplicatively coupled fluctuating forces is studied analytically and numerically in quantitative detail in the range of control parameter r where the unforced system shows the first transcritical and the first pitchfork bifurcation.