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=rtxt(1-xt), where rt 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. © 1989 The American Physical Society