Fuzzy cyclic modeling of a periodically perturbed pendulum

This paper extends a product-space clustering method, the bisection and homogeneity algorithm, to the cyclic modeling of a periodically perturbed pendulum. The algorithm creates a structural decomposition of the state space for each drive cycle of the vertical support. Smooth trajectory approximations of chaotic behavior are the result of combining multiple SAM/COG systems with a one-step Euler´s method. Experimental results suggest that a finer phase partitioning is necessary and sufficient for the fuzzy model to preserve the periodicity of the vertical drive