Modulated nonlinear processes and a novel mechanism to induce chaos

Many natural phenomena are governed by nonlinear recursive relations of the type xₜ₊₁=f(xₜ), where f does depend on t. We focus our interest on the particularly simple case xₜ₊₁=rₜ{x}ₜ$(1-${x}ₜ$), where ${r}ₜ$ adopts either periodically or at random the values A and B. Graphical representations of the Lyapunov exponent on the AB plane show unexpected features, like self-similarity and early chaos (i.e., chaos for very low parameter values). In relation with the latter we discuss a novel mechanism to induce chaotic behavior. The meaning of the Lyapunov exponent for random processes is examined.