A New Theory of Fuzzy Chaos for Simulation of Non-Linear Dynamical Systems
We describe in this chapter 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 identification 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 new theory of Fuzzy Chaos, where we can use fuzzy sets to describe the behaviors of a system. We can also use fuzzy logic to build rules for behavior identification, using the mathematical knowledge from dynamical systems theory.
KeywordsFractal Dimension Membership Function Fuzzy Logic Lyapunov Exponent Fuzzy Rule
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