Sensitivity, Shadowing Property and P-Chaos in Duopoly Games

• DOI: 10.3390/sym17040511
• Publication Date: 2025-03-28T10:06:35Z
• Authors: Hongqing Wang; Tianxiu Lu; Risong Li; Ping Gao
• Keywords: Duopoly

In this paper, we discussed the cofinite sensitivity, shadowing property (SP), P-chaos, and chain mixing of a system induced by symmetric maps (Cournot maps) D(a,b)=(t(b),s(a)) over product space G×H, where s:G→H, t:H→G, a∈G, b∈H, G H are closed subintervals with G,H⊂R. The following hold: (1) D is cofinitely sensitive equivalent to D2|Γ1 or D2|Γ2 being sensitive, Γ1={(t(b),b):b∈H}, Γ2={(a,s(a)):a∈G}. (2) possessing an SP both s∘t t∘s having SP. (3) possesses if only does as well. (4) P-chaotic P-chaotic. (5) If mixing, then mixing. (6) transitive. Moreover, extended (1)–(4) three-dimensional cases.