Bifurcation Structure in a Model of Monetary Dynamics with Two Kink Points

In the present paper we consider the discrete version of the Sargent & Wallace (Econometrica 41:1043–8, 1973) model with perfect foresight. We assume a piecewise linear money demand function, decreasing over a ‘normal’ range (−aR,aL) and constant when the expected inflation rate is beyond these bounds. In this way we obtain that the monetary dynamics are described by a one-dimensional map having two kink points. We show that when the slope of the money demand function (μ) is sufficiently large in absolute value and the speed of adjustment of the price to the market disequilibrium (α) is smaller than 1 either cycles of any period or chaotic dynamics may be generated by the model. The description of the bifurcation structure of the (α,μ) parameter plane is given

Global dynamic scenarios in a discrete-time model of renewable resource exploitation: a mathematical study

We consider the two-dimensional map introduced in Bischi et al. (J Differ Equ Appl 21(10):954–973, 2015) formulated as a model for a renewable resource exploitation process in an evolutionary setting. The global dynamic scenarios displayed by the model are not so often encountered in smooth two-dimensional dynamical systems. We explain the occurrence of such scenarios at the light of the theory of noninvertible maps. Moreover, complex structures of basins of attraction of coexisting invariant sets are observed. We analyze such structures by examining stability properties of chaotic sets, in the case in which a non-topological Milnor attractor is present. Stability changes of a chaotic set occur through global bifurcations (such as riddling and blowout) and are detected by means of the study of the spectrum of Lyapunov exponents associated with the set