... studies the intrinsically nonlinearlink between signal and noise in a variety of systems. The word stochasticresonance has been coined to describe situations in which the noise can benefitthe information-carrying ... dx,meaning o(dx)/dx is again in nitesimal. In other words, the derivative f(x),independent of dx, is in nitely close tof(x+dx)−f(x)dxfor all in nitesimalsdx. The modern definition, as ... (5 5) The solution isy(b)=a≤x≤b(1 + r(x)dx).y(a). (5 6) What is the meaning of this product? Putting (x)=r(x)dx, an in nitesimal, and expanding the product as in (4 7), we getx(1 + (x))...