Related papers: Stability and bifurcation in network traffic flow:…

Understanding traffic statics and dynamics in urban networks is critical to develop effective control and management strategies. In this paper, we provide a novel approach to study the traffic statics and dynamics in a signalized…

We consider a discrete-time dynamical system in a car-following context. The system was recently introduced to parsimoniously model human driving behavior based on utility maximization. The parameters of the model were calibrated using…

Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we first introduce a continuous multi-commodity kinematic wave…

Poincar\'e maps play a fundamental role in nonlinear dynamics and chaos theory, offering a means to reduce the dimensionality of continuous dynamical systems by tracking the intersections of trajectories with lower-dimensional section…

We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…

This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…

The Poincar\'e map is widely used to study the qualitative behavior of dynamical systems. For instance, it can be used to describe the existence of periodic solutions. The Poincar\'e map for dynamical systems with impulse effects was…

We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…

Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence…

We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

We study an interplay between delay and discontinuous hysteresis in dynamical systems. After having established existence and uniqueness of solutions, we focus on the analysis of stability of periodic solutions. The main object we study is…

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…

This work studies two types of computer networking models. The primary focus is to understand the different dynamical phenomena observed in practice due to the presence of severe nonlinearities, delays and widely varying operating…

A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and…

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…

In this work, our primary goal is to study the Poincare map and the existence of limit cycles for Welander's model that describes ocean convection. Welander developed two versions of his model, one with a smooth transition between…

A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…

This paper deals with existence and robust stability of hybrid limit cycles for a class of hybrid systems given by the combination of continuous dynamics on a flow set and discrete dynamics on a jump set. For this purpose, the notion of…