Distributional chaos of Cournot maps (Q2770156)

A class of two-dimensional maps on a unit interval, called Cournot maps, is investigated. They model a competitive economic process known as Cournot duopoly. Among various measures of chaos for dynamical systems on the interval [\textit{B. Schweizer} and \textit{J. Smítal}, Trans. Am. Math. Soc. 344, No. 2, 737-754 (1994; Zbl 0812.58062)], the distributional chaos or Li-Yorke chaos appear to be most appropriate for continuous maps, it is proved that a Cournot map has positive topological entropy if and only if it is distributionally chaotic.