Danca, Marius-F.; Chen, Guanrong Bifurcation and chaos in a complex model of dissipative medium. (English) Zbl 1129.37314 Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 10, 3409-3447 (2004). Summary: We carefully reexamine the chaotic RF model, first studied by M. I. Rabinovich and A. L. Fabrikant [Sov. Phys. JETP 50, 311–317 (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. Cited in 2 ReviewsCited in 10 Documents MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 34C23 Bifurcation theory for ordinary differential equations 37G99 Local and nonlocal bifurcation theory for dynamical systems Keywords:Bifurcation; chaos; iterative linearization method Software:Turbo Pascal PDFBibTeX XMLCite \textit{M.-F. Danca} and \textit{G. Chen}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 10, 3409--3447 (2004; Zbl 1129.37314) Full Text: DOI References: [1] DOI: 10.1142/3033 [2] DOI: 10.1007/s002110050100 · Zbl 0822.65048 [3] Rabinovich M. I., J. E. T. P. (Sov.) 77 pp 617– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.