Anderson, Douglas R.; Myran, Nicholas G.; White, Dustin L. Basins of attraction in a Cournot duopoly model of Kopel. (English) Zbl 1111.39010 J. Difference Equ. Appl. 11, No. 10, 879-887 (2005). Authors’ abstract: For a nonlinear Cournot duopoly map of M. Kopel [Chaos Solitons Fractals 7, No. 12, 2031–2048 (1996; Zbl 1080.91541)], we show that a circle, lines, and rectangles play a key role in determining the basins of attraction in the case of three nontrivial Nash equilibria. Reviewer: Yuming Chen (Waterloo) Cited in 6 Documents MSC: 39A12 Discrete version of topics in analysis 39A10 Additive difference equations 37B25 Stability of topological dynamical systems 37C70 Attractors and repellers of smooth dynamical systems and their topological structure Keywords:discrete dynamical systems; asymptotic behavior; fixed point; attractor; repeller; Cournot duopoly map; basins of attraction; Nash equilibria Citations:Zbl 1080.91541 PDFBibTeX XMLCite \textit{D. R. Anderson} et al., J. Difference Equ. Appl. 11, No. 10, 879--887 (2005; Zbl 1111.39010) Full Text: DOI References: [1] DOI: 10.1201/9781420035353 · doi:10.1201/9781420035353 [2] Cournot A., Recherche sur la Principes Matematiques de la Theorie de las Richesse (1838) [3] DOI: 10.1016/S0960-0779(96)00070-7 · Zbl 1080.91541 · doi:10.1016/S0960-0779(96)00070-7 [4] DOI: 10.1016/S0960-0779(98)00210-0 · Zbl 0955.37022 · doi:10.1016/S0960-0779(98)00210-0 [5] DOI: 10.1016/S0167-2681(01)00188-3 · doi:10.1016/S0167-2681(01)00188-3 [6] DOI: 10.1016/S0960-0779(98)00130-1 · Zbl 0960.91017 · doi:10.1016/S0960-0779(98)00130-1 [7] DOI: 10.1007/978-1-4419-8732-7 · Zbl 0855.58042 · doi:10.1007/978-1-4419-8732-7 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.