Related papers: Stability and bifurcation in network traffic flow:…
We study a robust control problem for dynamical flow networks. In the considered dynamical models, traffic flows along the links of a transportation network --modeled as a capacited multigraph-- and queues up at the nodes, whereby control…
In this paper we investigate the relation between robustness of periodic orbits exhibited by systems with impulse effects and robustness of their corresponding Poincar\'e maps. In particular, we prove that input-to-state stability (ISS) of…
This paper examines the IDM microscopic car-following model from a dynamical systems perspective, analyzing the effects of delay on congestion formation. Further, a case of mixed-autonomy is considered by controlling one car with…
We discuss the appearance of oscillatory and standing wave states in second-order oscillator networks showing that it is a special case of a more general mechanism involving secondary synchronized clusters induced by inertia. Using a…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
There are few examples of non-autonomous vector fields exhibiting complex dynamics that may be proven analytically. We analyse a family of periodic perturbations of a weakly attracting robust heteroclinic network defined on the two-sphere.…
Stop-and-go waves are commonly observed in traffic and pedestrian flows. In most traffic models they occur through a phase transition after fine tuning of parameters when the model has unstable homogeneous solutions. Inertia effects are…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
We prove dynamical stability and instability theorems for Poincar\'{e}-Einstein metrics under the Ricci flow. Our key tool is a variant of the expander entropy for asymptotically hyperbolic manifolds, which Dahl, McCormick and the first…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
The flow past a bullet-shaped blunt body moving in a pipe is investigated through global linear stability analysis (LSA) and direct numerical simulation (DNS). A cartography of the bifurcation curves is provided thanks to LSA, covering the…
In 2010s Fleiner introduced a notion of stable flows in directed networks and showed that such a flow always exists and can be found by use of a reduction to the stable allocation problem due to Baiou and Balinski. Recently Cseh and…
Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of…
It is presently believed that flows of viscoelastic polymer solutions in geometries such as a straight pipe or channel are linearly stable. Here we present experimental evidence that such flows can be nonlinearly unstable and can exhibit a…
The first stages of the path instability phenomenon known to affect the buoyancy-driven motion of gas bubbles rising in weakly or moderately viscous liquids are examined thanks to a recently developed numerical tool designed to assess the…
Using various techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al., Nature, 526:550-553, 2015], which describes the rise of turbulent pipe flow via a PDE system of reduced…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…