Global InformationHyperchaos information
A hyperchaotic system is a dynamical system with a bounded attractor set, on which there are at least two positive Lyapunov exponents.[1]
Since on an attractor, the sum of Lyapunov exponents is non-positive, there must be at least one negative Lyapunov exponent. If the system has continuous time, then along the trajectory, the Lyapunov exponent is zero, and so the minimal number of dimensions in which continuous-time hyperchaos can occur is 4.
Similarly, a discrete-time hyperchaos requires at least 3 dimensions.
- ^ Letellier, Christophe; Rossler, Otto E. (2007-08-05). "Hyperchaos". Scholarpedia. 2 (8): 1936. doi:10.4249/scholarpedia.1936. ISSN 1941-6016.