In this paper, a duopoly airlines bidding game model based on nonlinear variable cost is built, then local and global dynamic characteristics of this bidding game model are extensively researched, with the purpose of discussing the influences of price adjustment speed and of price elasticity coefficient on the evolving regularity of bidding competition of airline. We study the model from both theoretical and numerical simulation aspects. The local and global properties of the model in two-parameter space are analyzed. Moreover, we systematically research the regularity of dynamic evolution about attractors and topological structures of attractors in symmetric and asymmetric information. The simulation results show that there are local steady and multi-steady in this nonlinear model. The adjustment speed and price elasticity coefficient do have significant effects on the model, specifically, once the adjustment speed and price elasticity coefficient exceed the threshold, the game model will irreversibly enter into chaotic state after multiple bifurcations. Furthermore, the speed of price adjustment and the coefficient of price sensitivity have a significant impact on the nonlinear game model. Even subtle changes can cause the system enter bifurcation phenomenon so far as to chaos state. Therefore, the airlines need prudently adjust the parameters of game model in order to keep market competition in steady state in the long run.

本文建立了一种基于非线性可变成本的双寡头航空公司竞价博弈模型，然后对该竞价博弈模型的局部和全局动态特性进行了广泛研究，以期探讨价格调整速度和价格弹性系数对竞价博弈的影响。航空公司竞标竞争的发展规律。我们从理论和数值模拟两个方面研究模型。分析了该模型在两参数空间中的局部和全局性质。此外，我们系统地研究了对称和不对称信息中吸引子的动态演化规律和吸引子的拓扑结构。仿真结果表明，该非线性模型具有局部稳态和多稳态。调整速度和价格弹性系数确实会对模型产生重大影响，具体而言，一旦调整速度和价格弹性系数超过阈值，博弈模型将在多次分叉后不可逆地进入混沌状态。此外，价格调整的速度和价格敏感性系数对非线性博弈模型具有重要影响。甚至细微的变化都可能导致系统进入分叉现象，甚至达到混乱状态。因此，航空公司需要谨慎地调整博弈模型的参数，以长期保持市场竞争处于稳定状态。在多次分叉之后，游戏模型将不可逆转地进入混乱状态。此外，价格调整的速度和价格敏感性系数对非线性博弈模型具有重要影响。甚至细微的变化都可能导致系统进入分叉现象，直至达到混乱状态。因此，航空公司需要谨慎地调整博弈模型的参数，以长期保持市场竞争处于稳定状态。在多次分叉之后，游戏模型将不可逆转地进入混乱状态。此外，价格调整的速度和价格敏感性系数对非线性博弈模型有重要影响。甚至细微的变化都可能导致系统进入分叉现象，甚至达到混乱状态。因此，航空公司需要谨慎地调整博弈模型的参数，以长期保持市场竞争处于稳定状态。