In this paper, we carefully reexamine the chaotic RF model, first studied by Rabinovich and Fabrikant [1979], and have found many new and rich complex dynamics of the model that were mostly not reported before. The chaotic RF model has proved to be a great challenge to classical numerical methods, in the sense that most classical numerical methods have not been very successful in the study of complex dynamics of this special RF model. Therefore, in this paper, we present and apply a special numerical method, the Local Iterative Linearization (LIL) method, along with a special Turbo Pascal code based on this accurate LIL algorithm, for a careful numerical study of this complex RF model. Many interesting new findings are summarized and reported in this paper.
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