Border Collision Bifurcations in a Footloose Capital Model with First Nature Firms

Abstract

In this paper we extend the discrete time Footloose Capital model analyzed in Commendatore et al. (Nonlinear Dyn Psychol Life Sci 11(2):267---289, 2007) by introducing "first nature firms", i.e., firms that use locally specific blueprints and, therefore, are immobile. Due to the presence of first nature firms (symmetrically distributed across the regions), the central dynamic map becomes a piecewise differentiable function: in addition to "standard" flip and pitchfork bifurcations also border collision bifurcations are possible and instances of multistability may emerge. Our analysis confirms and extends the results of Commendatore et al. (2007): (1) continuous time formulation hides complex dynamics patterns; (2) asymmetric distributions of industrial activity can be endogenously generated and are path dependent.