From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

Figure 2

Bifurcation digrams of (a) logistic map, (b) tent map, (c) Gaussian map, and (d) Hénon map. Parameter in logistic map can be set at ; chaos happens when in (a). Parameter in tent map can be set at ; chaos happens when in (b). Parameter in tent map can be set at ; chaos happens when and in (c). Parameters and are a classic setting in Hénon map; one of its invariant points on the attractor, and , can be used as an initial value setting.

(a) Logistic map

(b) Tent map

(c) Gaussian map

(d) Hénon map