TY - JOUR
T1 - Dynamics of a generalized fashion cycle model
AU - Sushko, Iryna
AU - Gardini, Laura
AU - Matsuyama, Kiminori
PY - 2019
Y1 - 2019
N2 - We study a four-parameter family of 2D piecewise linear maps with two discontinuity lines. This family is a generalization of the discrete-time version of the fashion cycle model by Matsuyama, which was originally formulated in continuous time. The parameter space of the considered map is characterised by quite a complicated bifurcation structure formed by the periodicity regions of various attracting cycles. Besides the standard period adding and period incrementing structures, there exist incrementing structures with some distinctive properties, as well as novel mixed structures, which we study in detail. The boundaries of many periodicity regions associated with border collision bifurcations of the related cycles are obtained analytically. Several mixed structures are qualitatively described.
AB - We study a four-parameter family of 2D piecewise linear maps with two discontinuity lines. This family is a generalization of the discrete-time version of the fashion cycle model by Matsuyama, which was originally formulated in continuous time. The parameter space of the considered map is characterised by quite a complicated bifurcation structure formed by the periodicity regions of various attracting cycles. Besides the standard period adding and period incrementing structures, there exist incrementing structures with some distinctive properties, as well as novel mixed structures, which we study in detail. The boundaries of many periodicity regions associated with border collision bifurcations of the related cycles are obtained analytically. Several mixed structures are qualitatively described.
KW - 2D discontinuous piecewise linear map
KW - Border collision bifurcation
KW - Fashion cycle model
KW - Period adding bifurcation structure
KW - Period incrementing bifurcation structure
KW - 2D discontinuous piecewise linear map
KW - Border collision bifurcation
KW - Fashion cycle model
KW - Period adding bifurcation structure
KW - Period incrementing bifurcation structure
UR - http://hdl.handle.net/10807/274814
U2 - 10.1016/j.chaos.2019.06.006
DO - 10.1016/j.chaos.2019.06.006
M3 - Article
SN - 0960-0779
VL - 126
SP - 135
EP - 147
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -