Complexity Analysis of a 2D-Piecewise Smooth Duopoly Model: New Products versus Remanufactured Products

Abstract

Recent studies on remanufacturing duopoly games have handled them as smooth maps and have observed that the bifurcation types that occurred in such maps belong to generic classes like period-doubling or Neimark-Sacker bifurcations. Since those games yield piecewise smooth maps, their bifurcations belong to the so-called border-collision bifurcations, which occur when the map’s fixed points cross the borderline between the smooth regions in the phase space. In the current paper, we present a proper systematic analysis of the local stability of the map’s fixed points both analytically and numerically. This includes studying the border-collision bifurcation depending on the map’s parameters. We present different multistability scenarios of the dynamics of the game’s map and show different types of periodic cycles and chaotic attractors that jump from one region to another or just cross the borderline in the phase space.