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On growing through cycles: Matsuyama’s M-map and Li–Yorke chaos

Liuchun Deng and M. Khan ()

Journal of Mathematical Economics, 2018, vol. 74, issue C, 46-55

Abstract: Recent work of Gardini et al. (2008), building on earlier work of Mitra (2001) and Mukherji (2005), considers the so-called M-map that generates a dynamical system underlying Matsuyama’s (1999) endogenous growth model. We offer proofs of the fact that there do not exist 3- or 5-period cycles in the M-map, and an example (a numerical proof) of the existence of a 7-period cycle. We use the latter, and a construction in Khan and Piazza (2011), to identify a range of parameter values of the M-map that guarantee the existence of cycles of all periods, except 3 and 5. Our argumentation relies on, and reports, the first four iterations of the M-map that may have independent interest.

Keywords: Matsuyama’s model; Iterations; Li–Yorke chaos; KP-construction; 3-period; Cycles (search for similar items in EconPapers)
Date: 2018
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Handle: RePEc:eee:mateco:v:74:y:2018:i:c:p:46-55