A theory of fuzzy chaos for the simulation and control of non-linear dynamical systems

We describe in this paper a new theory of chaos using fuzzy logic techniques. Chaotic behavior in non-linear dynamical systems is very difficult to detect and control. Part of the problem is that mathematical results for chaos are difficult to use in many cases, and even if one could use them there is an underlying uncertainty in the accuracy of the numerical simulations of the dynamical systems. For this reason, we can model the uncertainty of detecting the range of values where chaos occurs, using fuzzy set theory. Using fuzzy sets, we can build a theory of Fuzzy Chaos, where we can use fuzzy sets to describe the behaviors of a system. We illustrate our approach with two cases: Chua's circuit and Duffing's oscillator.