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.
Original language | English (US) |
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Pages (from-to) | 299-309 |
Number of pages | 11 |
Journal | Chaos, Solitons and Fractals |
Volume | 91 |
DOIs | |
State | Published - Oct 1 2016 |
Keywords
- Border collision bifurcation
- Codimension-two bifurcation
- Homoclinic bifurcation
- One-dimensional piecewise smooth map
- Robust chaos
- Skew tent map
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics