Linear, Random Representations of Chaos

Although there may be some disagreement as to the precise definition of chaos, it is generally characterized as a nonlinear, deterministic phenomenon. For a class of common chaotic systems, this paper introduces equivalent descriptions in the form of linear, time-invariant (LTI) systems with random inputs. Such models have many advantages as they are much better matched to traditional signal and system theory. The outputs of these LTI systems will be shown to be indistinguishable from the outputs of the corresponding chaotic systems. Specifically, for a given random input the LTI system will generate exactly the same output as the corresponding chaotic map with a certain initial condition