Conclusions p] In a classical model of business cycle, we introduce parameters depending on time, producing a non-autonomous linear second order difference equation, which is analyzed in the setting of non-autonomous discrete systems. Roughly speaking, one could think on a linear model whose parameters are pertubed is some way, for instance a random way.
The stability and limit set of the orbits of the non-autonomous system associated to the difference equation are studied. When all the maps of the system are contractive, then the system is stable, producing bounded orbits. in other cases, some simulations shows that when we have expansive maps in the system, unbounded orbits and some type of chaotic behaviour may appear. It must be pointed out that the chaotic behaviour appear when both, contractive and expansive maps are in the system infinitely many times.
It is an interesting question to analyze these type of “chaotic orbits”, that is: are they really chaotic in some theoretical sense?
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Cánovas Peña, J.S., Marín, M.R. (2006). Non-Autonomous Business Cycle Model. In: Puu, T., Sushko, I. (eds) Business Cycle Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32168-3_6
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DOI: https://doi.org/10.1007/3-540-32168-3_6
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