We develop a nonlinear dynamic Cournot duopoly model in discrete time, where two bounded rational quantity-setting firms, both endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. One of the two competing firms adopts best-reply behaviour, whereas...

The phenomenon of synchronization of a two-dimensional discrete dynamical system is studied for the model of an economic duopoly game, whose time evolution is obtained by the iteration of a noninvertible map of the plane. In the case of identical players the map has a symmetry property that...

In this paper we consider a discontinuous one-dimensional piecewise linear model describing a neoclassical growth model. These kind of maps are widely used in the applied context. We determine the analytical expressions of border collision bifurcation curves, responsible for the observed...

In this paper we consider a continuous one-dimensional map, which is linear on one side of a generic kink point and hyperbolic on the other side. This kind of map is widely used in the applied context. Due to the simple expression of the two functions involved, in particular cases it is possible...

Rational expectations models have increasingly been replaced by models with various forms of learning. This paper studies the global dynamics of a model of renewable resource markets due to Hommes and Rosser [Macroecon. Dyn. 5 (2001) 180] under adaptive and statistical learning systems. The...

In this paper, we consider a two-dimensional map (a duopoly game) in which the fixed point is destabilized via a subcritical Neimark–Hopf (N–H) bifurcation. Our aim is to investigate, via numerical examples, some global bifurcations associated with the appearance of repelling closed...

We present a simple financial market model with interacting chartists and fundamentalists. Since some speculators only become active when a certain misalignment level has been crossed, the model dynamics is driven by a discontinuous piecewise linear map. Recent mathematical techniques allow a...