Autonomous choices among deterministic evolution-laws as source of uncertainty

Abstract

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these pseudo-random dynamical systems. Each chaotic system in this family exhibits a sensitivity to initial conditions that encompasses the sequence of choices of the evolution rule in some collection of maps. This opens a possibility to extend current theories of complex behaviors on the basis of intrinsic uncertainty in deterministic chaos.