Bifurcation and Chaos in a Complex Model of dissipative Medium

In this paper, we carefully re-examine the chaotic RF model, first studied by Rabinovich & Fabrikant [1979], and 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 studying the complex dynamics of this special RF model. Therefore, in this paper, we develop 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.