Subcritical Hopf bifurcations in a car-following model with reaction-time delay
نویسنده
چکیده
A nonlinear car-following model of highway traffic is considered, which includes the reaction-time delay of drivers. Linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via Hopf bifurcations and thus oscillations can appear. The stability and amplitudes of the oscillations are determined with the help of normal-form calculations of the Hopf bifurcation that also handles the essential translational symmetry of the system. We show that the subcritical case of the Hopf bifurcation occurs robustly, which indicates the possibility of bistability. We also show how these oscillations lead to spatial wave formation as can be observed in real-world traffic flows.
منابع مشابه
Hopf Calculations in Delayed Car-following Models
A nonlinear car-following model that includes the reaction-time delay of drivers is considered. When investigating the linear stability of the uniform flow solution, boundaries of Hopf bifurcations are determined in the parameter space. Crossing these boundaries, oscillations may appear corresponding to travelling wave solutions. Hopf normal form calculations prove robustly subcritical behavior...
متن کاملDelay Induced Subcritical Hopf Bifurcation in a Diffusive Predator-prey Model with Herd Behavior and Hyperbolic Mortality∗
In this paper, we consider the dynamics of a delayed diffusive predator-prey model with herd behavior and hyperbolic mortality under Neumann boundary conditions. Firstly, by analyzing the characteristic equations in detail and taking the delay as a bifurcation parameter, the stability of the positive equilibria and the existence of Hopf bifurcations induced by delay are investigated. Then, appl...
متن کاملA THREE DIMENSIONAL HTLV-1 MODEL WITH INTRACELLULAR AND IMMUNE ACTIVATION DELAYS
In this paper, a three dimensional mathematical model for HTLV-1infection with intracellular delay and immune activation delay is investigated.By applying the frequency domain approach, we show that time delays candestabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and sta-ble or unstable periodic oscillations. At the end, numerical simulations areillustrated.
متن کاملHopf bifurcations in time-delay systems with band-limited feedback
We investigate the steady-state solution and it’s bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed feedback. We show that the steady state is globally stable for small feedback gain and that local stability is lost, generically, through a Hopf bifurcation...
متن کاملUsing the Reaction Delay as the Driver Effects in the Development of Car-Following Models
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 ...
متن کامل