TY  - JOUR
AU  - Amira, Rami
AU  - Abdelouahab, Mohammed Salah
AU  - Touafek, Nouressadat
AU  - Mesmouli, Mouataz Billah
AU  - Zaidi, Hasan Nihal
AU  - Hassan, Taher S.
PY  - 2024
TI  - Nonlinear dynamic in a remanufacturing duopoly game: spectral entropy analysis and chaos control
JO  - AIMS Mathematics
SP  - 7711
EP  - 7727
VL  - 9
IS  - 3
AB  - In this study, our focus is on stabilizing a competitive game involving an original equipment manufacturer (OEM) and a third-party remanufacturer (TPR). To assess the presence of chaos within the dynamics of this game, we employ various analytical tools, including spectral entropy (SE), bifurcation diagrams, and Lyapunov exponents. The unpredictable nature of chaotic dynamics significantly influences the market and has negative implications for the strategic decisions of both firms. Our approach to counteracting this chaotic behaviour and stabilizing the system revolves around the implementation of the Ott, Grebogi, and Yorke (OGY) method. Crucially, our analysis highlights that the marginal costs (       c    n   and        c    r  ) incurred by the OEM and TPR emerge as pivotal factors in achieving stabilization within the game. To provide a tangible demonstration of the effectiveness of our proposed stabilization strategy in the context of this competitive environment, we conducted numerical simulations.
UR  - https://doi.org/10.3934/math.2024374
DO  - 10.3934/math.2024374