TY - JOUR A2 - Elsadany, Abdelalim AU - Tu, Hongliang AU - Zhan, Xueli AU - Mao, Xiaobing PY - 2017 DA - 2017/10/22 TI - Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities SP - 7384150 VL - 2017 AB - We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos. SN - 1026-0226 UR - https://doi.org/10.1155/2017/7384150 DO - 10.1155/2017/7384150 JF - Discrete Dynamics in Nature and Society PB - Hindawi KW - ER -