TY - JOUR
T1 - Chaotic dynamics in a three-dimensional map with separate third iterate: The case of Cournot duopoly with delayed expectations
AU - Bignami, Fernando
AU - Agliari, Anna
PY - 2018
Y1 - 2018
N2 - We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We assume that both producers have naive expectations but one of them reacts with delay to the move of its competitors, due to a “less efficient” production process of a competitor with respect to its opponent. The model is described by a 3D map having the so-called “cube separate property” that is its third iterate has separate components. We show that many cycles may coexist and, through global analysis, we characterize their basins of attraction. We also study the chaotic dynamics generated by the model, showing that the attracting set is either a parallelepiped or the union of coexisting parallelepipeds. We also prove that such attracting sets coexist with chaotic surfaces, having the shape of generalized cylinders, and with different chaotic curves.
AB - We consider a Cournot duopoly with isoelastic demand function and constant marginal costs. We assume that both producers have naive expectations but one of them reacts with delay to the move of its competitors, due to a “less efficient” production process of a competitor with respect to its opponent. The model is described by a 3D map having the so-called “cube separate property” that is its third iterate has separate components. We show that many cycles may coexist and, through global analysis, we characterize their basins of attraction. We also study the chaotic dynamics generated by the model, showing that the attracting set is either a parallelepiped or the union of coexisting parallelepipeds. We also prove that such attracting sets coexist with chaotic surfaces, having the shape of generalized cylinders, and with different chaotic curves.
KW - 3D nonlinear discrete maps
KW - Bifurcation analysis
KW - Chaotic dynamics
KW - Coexistence of attractors
KW - Mathematics (all)
KW - 3D nonlinear discrete maps
KW - Bifurcation analysis
KW - Chaotic dynamics
KW - Coexistence of attractors
KW - Mathematics (all)
UR - http://hdl.handle.net/10807/121360
U2 - 10.1016/j.chaos.2018.03.023
DO - 10.1016/j.chaos.2018.03.023
M3 - Article
SN - 0960-0779
VL - 110
SP - 216
EP - 225
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -