Dynamic effects of memory in a cobweb model with competing technologies

We analyze a simple model based on the cobweb demand–supply framework with costly innovators and free imitators and study the endogenous dynamics of price and firms’ fractions in a homogeneous good market. The evolutionary selection between technologies depends on a performance measure in which a memory parameter is introduced. The resulting dynamics is then described by a two-dimensional map. In addition to the locally stabilizing effect due to the presence of memory, we show the existence of a double stability threshold which entails for different dynamic scenarios occurring when the memory parameter takes extreme values (i.e. when consideration of the last profit realization prevails or it is too much neglected). The eventuality of different coexisting attractors as well as the structure of the basins of attraction that characterizes the path dependence property of the model with memory is shown. In particular, through global analysis we also illustrate particular bifurcations sequences that may increase the complexity of the related basins of attraction.