Search

With the rise of the sharing economy, shared bicycles have become an important component of urban transportation. This paper explores the nonlinear dual oligopoly system for the Cournot model in the bike-sharing market; both operators have maximized profits as their competitive goals. The analysis of pivotal factors influencing passenger preferences, including pricing discounts and comfort levels, is meticulously depicted by a bifurcation diagram. A new chaotic attractor—the shared bicycle attractor—is discovered. The research results indicate that larger discounts and adjustment speeds can cause the system to be in a chaotic state, which is not conducive to the long-term development of operators, although discounts can indeed attract more passengers to a certain extent. On the other hand, the increase in the marginal cost of comfort loss can also make it difficult for enterprises to operate, which requires continuous technological innovation to improve the comfort of cycling.

This paper develops a multi-objective optimization model for national high-speed railway network planning. Three objectives are proposed from the macro, meso, and micro perspectives, and these three objectives are considered simultaneously. Using real data, case studies are conducted to optimize China’s “four east–west and four north–south railway lines” network, which includes Beijing, Shanghai, Wuhan, Guangzhou, and Zhengzhou as main hubs. The results show that, on the one hand, the optimization model reduces the overlap between long-distance passengers and short-distance passengers on the high-speed railway line, facilitates the travel of passengers, and improves the line service capability; on the other hand, optimization of the network shortens the travel time of the passengers, reduces the cost of the railway, and improves the operation efficiency of the high-speed railway line network. The results show that the total travel time of all high-speed railway passengers in the optimization model is reduced by 18.4%, while the benefit rate of the operator increased by 21.99%.