Dynamics of a generalized fashion cycle model

Iryna Sushko, Laura Gardini () and Kiminori Matsuyama

Chaos, Solitons & Fractals, 2019, vol. 126, issue C, 135-147

Abstract: 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.

Keywords: Fashion cycle model; 2D discontinuous piecewise linear map; Border collision bifurcation; Period adding bifurcation structure; Period incrementing bifurcation structure (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:126:y:2019:i:c:p:135-147

DOI: 10.1016/j.chaos.2019.06.006

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