  An extensive statistical survey of universal approximators shows that as the
dimension of a typical dissipative dynamical system is increased, the number of
positive Lyapunov exponents increases monotonically and the number of parameter
windows with periodic behavior decreases. A subset of parameter space remains
in which topological change induced by small parameter variation is very
common. It turns out, however, that if the system's dimension is sufficiently
high, this inevitable, and expected, topological change is never catastrophic,
in the sense chaotic behavior is preserved. One concludes that deterministic
chaos is persistent in high dimensions.
