Car-following models, as the most popular microscopic traffic flow modeling, is increasingly being used by transportation experts to evaluate new Intelligent Transportation System (ITS) applications. A number of factors including individual differences of age, gender, and risk-taking behavior, have been found to influence car-following behavior. This paper presents a novel idea to calculate ...

We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A + A → A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximati...

In this article, we study a diffusive predator-prey system with prey-taxis under homogeneous Neumann boundary conditions. We establish the existence and boundedness of nonnegative global solutions. Through comparison without prey-taxis, find that positive constant equilibrium remains stable for while negative makes it unstable.