道路交通系统演化的非线性动力模型

为揭示各类交通规划管理政策和先进技术对道路交通系统的影响，构建了描述能源储备 量、机动车保有量和路网面积动态演化的三维非线性动力模型，重点对均衡解的存在性、唯一性 和稳定性进行分析。同时，通过数值试验验证了所得结论的正确性。结果表明：若所有变量及参 数为正，则有实际意义的均衡解唯一且稳定；若满足可供机动车行驶的能源增长率降低城镇开发 边界扩大、共享泊位供给量增加、机动车的平均能源消耗量增加中任一条件，则均衡平均车速提 高；当满足一定条件时，路网面积和路网容量的换算系数增加会提高均衡平均车速；存在最优行 驶机动车比例，可使均衡路网饱和度达到最低。

A Nonlinear Dynamic Model for Evolution of Road Traffic System

This study investigates the effect of various planning, management policies and advanced technologies on road traffic system. A three-dimensional nonlinear dynamic model is constructed to depict the dynamic evolutions of energy storage consumption, vehicle ownership and roadway area. The study analyzes the existence, uniqueness and stability of the equilibrium solution of the dynamic model, and verifies the correctness of the theoretical results through numerical experiments. The results indicate that: the equilibrium solution which has practical significance is unique and stable if all variables and parameters are strictly positive; the equilibrium average vehicle traveling speed increases when meet one of the following conditions : growth rate of energy available for vehicles decreases, the town development boundary, supply quantity of shared parking lots, or the average energy consumption of vehicles increases; when a certain condition is satisfied, the equilibrium average vehicle speed increases with the conversion coefficient between network area and road network capacity; there exists an optimal intensity of traffic volume, which could make the equilibrium road network reach its minimum saturation.