A Generative Traffic Flow Control Model based on Two-component Higher Order Camassa-Holm Systems

With the increasing prevalence of congestion control in transportation, the research on traffic flow prediction has received substantial attention recently. Nonlinear wave equations play an important role in the enhancement of traffic current and the prevention of the traffic congestion by nonlinear analysis. This paper deals with properties of solutions to a two-component higher order Camassa-Holm system. This system recovers many nonlinear wave equations which have been derived and applied as models describing the traffic instability and the evolution of traffic jam. To our best knowledge, propagation behaviours of the solution ρ and m have been proved, while the property of the solution u to this system has not been studied yet. Based on the family of diffeomorphisms, we prove that the solution u to this system loses instantly the compactness of its support. In this sense, the localized disturbance represented by the initial data u
₀
propagates with an infinite speed. Thus, we intend to describe the effect of initial small disturbance on the stability of traffic flows. Although the nontrivial solution u is no longer compactly supported, a detailed information about the nature of the solution is given by introducing a control function.