×

Basins of attraction in a Cournot duopoly model of Kopel. (English) Zbl 1111.39010

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.

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

Citations:

Zbl 1080.91541
PDFBibTeX XMLCite
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.