Persistent chaos in high dimensions.

ABSTRACT

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 where noncatastrophic topological change induced by a small parameter variation becomes inevitable. A geometric mechanism depending on dimension and an associated conjecture depict why topological change is expected but not catastrophic, thus providing an explanation of how and why deterministic chaos persists in high dimensions.