Related papers: Stability and bifurcation in network traffic flow:…
Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding is practically important for designing variable speed limit and ramp metering strategies. In this study, we attempt to develop a…
We analyze the dynamics of a deterministic model of inhibitory neuronal networks proving that the discontinuities of the Poincare map produce a never empty chaotic set, while its continuity pieces produce stable orbits. We classify the…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
In recent years the theory of border collision bifurcations has been developed for piecewise smooth maps that are continuous across the border, and has been successfully applied to explain nonsmooth bifurcation phenomena in physical…
We study traveling wave solutions of the Kerner--Konh\"auser PDE for traffic flow. By a standard change of variables, the problem is reduced to a dynamical system in the plane with three parameters. In a previous paper (Carrillo, F.A., J.…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to…
It is shown that in transient chaos there is no direct relation between averages in a continuos time dynamical system (flow) and averages using the analogous discrete system defined by the corresponding Poincare map. In contrast to…
Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subspaces. The usual method for analysing the stability of…
Traffic waves, known also as stop-and-go waves or phantom hams, appear naturally as traffic instabilities, also in confined environments as a ring-road. A multi-population traffic is studied on a ring-road, comprised of drivers with stable…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
The emergence dynamics of traffic instability has always attracted particular attention. For several decades, researchers have studied the stability of traffic flow using deterministic traffic models, with less emphasis on the presence of…
Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…
We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary…
The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing…
In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a…
Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…