Complex dynamics analysis for a remanufacturing duopoly model with nonlinear cost

Abstract

In this paper, a duopoly remanufacturing game of competition on output based on boundedly rational expectation is formulated. It involves an original equipment manufacturer (OEM) who makes new products and a third-party independent remanufacture (IR) who uses returned cores to produce differentiated products. Both parties adopt nonlinear cost functions. The study shows that consumer’s willingness-to-pay (WTP) has distinct effects on the OEM’s performance and the stability of Nash equilibrium. We present results on existence, stability and local bifurcations of the equilibrium points. Numerical simulations demonstrate that the system with varying model parameters may be driven to chaos and the loss of stability may be caused by period doubling bifurcations. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos.