Robust chaos in a credit cycle model defined by a one-dimensional piecewise smooth map

Iryna Sushko, Laura Gardini and Kiminori Matsuyama

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 299-309

Abstract: We consider a family of one-dimensional continuous piecewise smooth maps with monotone increasing and monotone decreasing branches. It is associated with a credit cycle model introduced by Matsuyama, under the assumption of the Cobb-Douglas production function. We offer a detailed analysis of the dynamics of this family. In particular, using the skew tent map as a border collision normal form we obtain the conditions of abrupt transition from an attracting fixed point to an attracting cycle or a chaotic attractor (cyclic chaotic intervals). These conditions allow us to describe the bifurcation structure of the parameter space of the map in a neighborhood of the boundary related to the border collision bifurcation of the fixed point. Particular attention is devoted to codimension-two bifurcation points. Moreover, the described bifurcation structure confirms that the chaotic attractors of the considered map are robust, that is, persistent under parameter perturbations.

Keywords: One-dimensional piecewise smooth map; Border collision bifurcation; Skew tent map; Homoclinic bifurcation; Robust chaos; Codimension-two bifurcation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:299-309

DOI: 10.1016/j.chaos.2016.06.015

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