Abstract
Nonlinear systems are important in many fields of science, mathematics, and engineering. The complexity of these systems, however, makes it difficult to ascertain their global behavior using classical methods of analysis. This is particularly true when the system is chaotic. In recent years, simple cell mapping (SCM) and generalized cell mapping (GCM) methods have been proposed and successfully used to analyze nonlinear systems. This paper combines fuzzy logic with cell to cell mapping techniques in order to analyze the global properties of nonlinear, dynamical systems. We refer to this new cell to cell mapping method as fuzzy cell mapping (FCM) to differentiate it from the other methods. Unlike SCM, FCM can handle chaotic systems and can do so without the added computational complexity required by GCM. In order to illustrate these different methods, we analyze a chaotic system using FCM and then compare our results with those obtained with SCM and GCM methods.
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