Period-3 doubling and chaotic attractors forα= 0.4. (a) Period-3 solution forf= 0.9868. (b) Period-6 solution forf= 1. (c) and (d) Chaotic attractors forf= 1.07 andf= 1.2 with the largest Lyapunov exponents 0.0805 and 0.0781, respectively.