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.

In many countries, public transport (PT) services are offered by multiple operators with different modes, such as trains, metros, and buses, which are interchangeable across a single journey. This paper presents a model with one origin (O)-destination(D) path operated by two operators, each of which is responsible for different parts of the OD journey. One operator competes with potential third-party transport companies by offering discount incentives. Such an abstract settings has not been discussed in the literature. We explore how prices, demand, profits, and social welfare change with discounts through a theoretical analysis and numerical simulations under five scenarios. The results indicate that in all the scenarios the operator offering a discount incentive can always attract more passengers and increase its profits. Moreover, reducing the service time of operators offering discounts contributes to an increase in social welfare. Notably, this paper deduces for the first time that the demand scenario aimed at maximizing social welfare is twice as high as that aimed at maximizing total profit. However, in the scenario of maximum social welfare, the profitability of operators becomes challenging.

Purpose: This paper aims to study the oscillation phenomenon before chaos as well as its mechanism of occurrence in the energy-saving and emission-reduction system.Design/methodology/approach: The system dynamics analysis, phase portrait analyses, equilibrium point analysis and bifurcation curve were applied to this paper.Findings: First, the authors find an oscillation phenomenon previous to chaos. Second, on the one hand, the existence of two unstable saddles is the reason for the occurrence of oscillation phenomenon. On the other hand, the increasing of carbon emissions can arouse oscillation phenomenon.Originality/value: This paper finds an oscillation phenomenon previous to chaos in the energy-saving and emission-reduction system. The mechanism of occurrence of oscillation phenomenon is studied. The existence of two unstable saddles is the reason for the occurrence of such oscillation phenomenon. The oscillation is related with fold bifurcation. The study also provides a theoretical basis for the further study of chaos control.

To address climate change and promote green and low‐carbon development, this study proposes an urban travel carbon footprint optimization method for transportation structures. Considering the environmental friendliness and efficiency of travel and combining carbon incentive policies and regret mechanisms, the travel preference model is constructed using game theory. Through the comprehensive perceived benefit function and multidimensional analysis, the effective reduction of travel carbon footprint is achieved. Taking Beijing as an example, the optimized transportation structure reduces the carbon footprint of travel by 17.17% and the total carbon emissions by 13.04%. Research has shown that to achieve the optimal carbon footprint, the green travel preference weight p ₁ in the multiobjective optimization model needs to be no less than 0.48, which verifies that this method can effectively alleviate the problem of transportation carbon emissions. Although this study has certain limitations in dynamic traffic demand applications, it has good practical application value for travel carbon footprint optimization under static demand conditions and contributes to the sustainable development of urban transportation and the realization of the “dual carbon” goals in China.

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%.