arXiv subjects

Yanghong Yu

Publications and source records attributed to Yanghong Yu.

3 recordsLinked to original sources

arXiv2026

When Entropy flows: drifting along the route to Chaos

Consider a smooth one-parameter family of vector fields defined over some smooth manifold transitions from order into chaos. Inspired by the Second law of Thermodynamics, one is led to ask: can we find a flow whose dynamics realize this transition? To answer this question, motivated by the Mallet-Yorke Orbit Index theory, the Arnold-Khesin scheme for hydrodynamics and a heuristic argument by Rene Thom, we introduce a construction that transforms any one-parameter family of vector fields into a new object: the "Entropy flow". The Entropy flow is a flow defined on the product of the phase space with the parameter space and is best thought of as a flow generated by the original one-parameter family together with a drift in the parameter space, that pushes the trajectory of a given initial condition into a disordered, more complex state. To exemplify, for the Period Doubling, the Ruelle-Takens-Newhouse and the Intermittency routes to chaos the Entropy flow behaves exactly as expected - that is, it truly pushes trajectories into more complex states. In addition, in the spirit of Forcing Theory, in the paper we use the Conley index to discuss how one can use the Entropy flow to study the connection between topology and bifurcations. Moreover, drawing on the numerical and analytic evidence, we will analyze how the Entropy flow behaves in several examples of famous flows, including the Lorenz system, the R\"ossler attractor, and the breakup of the Shilnikov homoclinic scenario.

math.DS↗

arXiv2024

Transition Matrix without Continuation in the Conley Index Theory

Given a one-parameter family of flows over a parameter interval $\Lambda$, assuming there is a continuation of Morse decompositions over $\Lambda$, Reineck defined a singular transition matrix to show the existence of a connection orbit between some Morse sets at some parameter points in $\Lambda$. This paper aims to extend the definition of a singular transition matrix in cases where there is no continuation of Morse decompositions over the parameter interval. This extension will help study the bifurcation associated with the change of Morse decomposition from a topological dynamics viewpoint.

math.DS↗

arXiv2024

Integrating optimal ridesharing matching into multimodal traffic model: Implications for policy and sustainable transport system

Integrating ridesharing matching explicitly into multimodal traffic models is crucial for accurately assessing the impacts of multimodal transport (MT) on urban economic and environmental aspects. This paper integrates an optimal ridesharing matching method into a path-based deterministic day-to-day traffic assignment framework, considers match cancellations, and captures the interactions between various modes on the road. The model incorporates five traffic modes (solo driving, ridesharing as a driver, ridesharing as a passenger, bus travel, and metro travel) and two groups of travelers based on their ownership status. Its steady state is determined through numerical experiments. The sensitivity analyses reveal that the MT system's performance varies with changes in ownership, bus fare, and ridesharing fare, demonstrating diverse impacts on mode split, travel cost, and emissions across different groups, road links, and regions. Our findings suggest that vehicle restrictions and pricing strategies have both benefits and drawbacks in managing MT system, emphasizing the need for careful consideration of trade-offs and social equity implications in policy-making and implementation. This study not only enhances the theoretical understanding of MT system but also provides valuable support for urban transportation policy-making aimed at achieving efficient, sustainable, and socially equitable transport systems.

physics.soc-ph↗