The dynamics of the NAIRU model with two switching regimes

Abstract

a b s t r a c tWe consider a model of inflation and unemployment proposed in Ferri et al. (JEBO, 2001), in which the dynamics are described by a discontinuous piecewise linear map, made up of two branches. We shall show that the bounded dynamics may be classified in two cases: we may have either regular dynamics with stable cycles of any period or quasiperiodic trajectories, or only chaotic dynamics (pure chaos in which a unique absolutely continuous invariant ergodic measure exists, and structurally stable), in a rich variety of cyclical chaotic intervals. The main results are the analytical formulation of the border collision bifurcation curves, through which we give a complete picture of the possible outcomes of the model.

On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders

“…For map (9) we consider restrictions s R > 1, s L > 1, m R < 0 and m L > 0, which corresponds to a situation in which type 1 chartists dominate type 1 fundamentalists but type 2 chartists are dominated by type 2 fundamentalists. Dynamically, only chaotic behavior can occur (a similar situation was considered in the paper by Tramontana et al (2010)). …”

“…It is also worth mentioning the works by Hommes (1991Hommes ( , 1995; Hommes and Nusse (1991) and Hommes et al (1995). Discontinuous models are furthermore discussed in Puu and Sushko (2002); Tramontana et al (2009Tramontana et al ( , 2010 and Bischi et al (2010).…”

A piecewise linear model of credit traps and credit cycles: a complete characterization

“…We have different structure of the basins depending on the two cases. That is, when there is bistability, then the structure of the basins is different depending on the condition determined with the straight line (r) given in (11), and the comments are similar to those already done for region A.…”

“…The dynamics of piecewise linear maps with one discontinuity point are well known in the case of slopes all smaller than one in modulus (see Leonov 1959;Leonov 1962;Keener 1980;Avrutin et al 2010;Gardini et al 2010, and applications to economics in Gardini et al 2011;Tramontana et al 2010;Tramontana et al 2011), and this is also relevant to our system. However, our system has two discontinuity points, which can be seen, for example, in Tramontana et al 2011.…”

“…in (26)) intersects the BCB curve Φ LR n given in (17) (resp. the BCB curve Φ LRL n−1 given in (23)) in a point of the straight line (r) given in (11). That is:…”