Swarm Intelligence

1.6 Chapter conclusion 11

• Henon Map: This map is a simplified version of the Poincare map of the Lorenz

system [27]. The Henon equations are given by

y(t) = 1 − a.y(t − 1) + z(t − 1) (1.31)

z(t) = b.y(t − 1) (1.32)

where a = 1.4 and b = 0.3 (the values for which the Henon map has a strange

attractor).

• Modified Henon map:

y1(k) = 1 − a(sin(y1(k − 1))) + by(k −1) (1.33)

y(k) = y1(k − 1) (1.34)

where k is the iteration number. This map is capable of generating chaotic attrac-

tors with multifolds via a period-doubling bifurcation route to chaos [34]. This

map exhibits very complicated dynamical behaviors with coexisting attractors.

The optimization algorithm ...