Superstable credit cycles and U-sequence

Iryna Sushko; Laura Gardini; Kiminori Matsuyama

doi:10.1016/j.chaos.2013.11.006

Superstable credit cycles and U-sequence

Iryna Sushko^*, Laura Gardini, Kiminori Matsuyama

^*Corresponding author for this work

Economics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model introduced by Matsuyama, where the map is defined over the absorbing interval via three functions, one of which is a constant. We show that the flat branch gives rise to superstable cycles whose periodicity regions are ordered according to a modified U-sequence and accumulate to the curves related to homoclinic cycles which represent attractors in Milnor sense. The boundaries of these regions correspond to fold and flip border collision bifurcations of the related superstable cycles.

Original language	English (US)
Pages (from-to)	13-27
Number of pages	15
Journal	Chaos, Solitons and Fractals
Volume	59
DOIs	https://doi.org/10.1016/j.chaos.2013.11.006
State	Published - Feb 2014

Funding

This work has been performed within the activity of the project PRIN 2009 “Local interactions and global dynamics in economics and finance: models and tools”, MIUR, Italy, and under the auspices of COST Action IS1104 “The EU in the new complex geography of economic systems: models, tools and policy evaluation”.

ASJC Scopus subject areas

Statistical and Nonlinear Physics
General Mathematics
General Physics and Astronomy
Applied Mathematics

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title = "Superstable credit cycles and U-sequence",

abstract = "We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model introduced by Matsuyama, where the map is defined over the absorbing interval via three functions, one of which is a constant. We show that the flat branch gives rise to superstable cycles whose periodicity regions are ordered according to a modified U-sequence and accumulate to the curves related to homoclinic cycles which represent attractors in Milnor sense. The boundaries of these regions correspond to fold and flip border collision bifurcations of the related superstable cycles.",

author = "Iryna Sushko and Laura Gardini and Kiminori Matsuyama",

note = "Funding Information: This work has been performed within the activity of the project PRIN 2009 “Local interactions and global dynamics in economics and finance: models and tools”, MIUR, Italy, and under the auspices of COST Action IS1104 “The EU in the new complex geography of economic systems: models, tools and policy evaluation”. ",

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AU - Gardini, Laura

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N2 - We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model introduced by Matsuyama, where the map is defined over the absorbing interval via three functions, one of which is a constant. We show that the flat branch gives rise to superstable cycles whose periodicity regions are ordered according to a modified U-sequence and accumulate to the curves related to homoclinic cycles which represent attractors in Milnor sense. The boundaries of these regions correspond to fold and flip border collision bifurcations of the related superstable cycles.

AB - We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model introduced by Matsuyama, where the map is defined over the absorbing interval via three functions, one of which is a constant. We show that the flat branch gives rise to superstable cycles whose periodicity regions are ordered according to a modified U-sequence and accumulate to the curves related to homoclinic cycles which represent attractors in Milnor sense. The boundaries of these regions correspond to fold and flip border collision bifurcations of the related superstable cycles.

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Superstable credit cycles and U-sequence

Abstract

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ASJC Scopus subject areas

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