Hyperchaos

The first two hyperchaotic systems were proposed in 1979.^[2] One is a discrete-time system ("folded-towel map"):

$${\displaystyle {\begin{aligned}&x_{t+1}=3.8x_{t}\left(1-x_{t}\right)-0.05\left(y_{t}+0.35\right)\left(1-2z_{t}\right),\\&y_{t+1}=0.1\left[\left(y_{t}+0.35\right)\left(1-2z_{t}\right)-1\right]\left(1-1.9x_{t}\right),\\&z_{t+1}=3.78z_{t}\left(1-z_{t}\right)+0.2y_{t}.\end{aligned}}}$$Another is a continuous-time system:$${\displaystyle {\begin{array}{ll}{\dot {x}}=-y-z,&{\dot {y}}=x+0.25y+w,\\{\dot {z}}=3+xz,&{\dot {w}}=-0.5z+0.05w.\end{array}}}$$More examples are found in.^[3]

Only a few experimental hyperchaotic behaviors have been identified.

Examples include in an electronic circuit,^[4] in a NMR laser,^[5] in a semiconductor system,^[6] and in a chemical system.^[7]