Nonlinear dynamics analysis and chaos control of price game among automobile manufacturers

With the large-scale promotion of new energy vehicles, automobile manufacturers are continuously lowering prices to compete for market share. This disorderly “price war” has made pricing strategies in the automobile market increasingly complex and dynamic. Under a multi-product duopoly market structure and based on the Hotelling spatial competition model, this study develops a dynamic Bertrand pricing game model composed of two battery electric vehicles (BEVs) and one plug-in hybrid electric vehicle (PHEV) under the carbon tax and dual credit policies. The dynamic characteristics of the three-dimensional discrete system are analyzed, including stability region, strange attractors and maximum Lyapunov exponent. The results show that: (1) Moderate price adjustments contribute more effectively to the long-term stability of the automobile market, and the stability region is the result of nonlinear coupling of the three. (2) Lower switching costs among automobile manufacturers can intensify market competition. (3) BEV manufacturers exhibit more stable pricing, indicating stronger market stability and guidance capability. Transforming manufacturers have steadier profits and stronger risk resistance, with PHEV pricing playing a key role in enhancing their competitiveness. (4) The dual credit policy regulates the market more effectively than the carbon tax policy. This study also identifies a “safe bottom line” of credit trading price for any level of carbon tax. (5) A composite control method of delayed feedback and state feedback is more effective for controlling the system.