Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.

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