Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8254543 | Chaos, Solitons & Fractals | 2016 | 11 Pages |
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
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Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Iryna Sushko, Laura Gardini, Kiminori Matsuyama,