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We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
A macroscopic model is proposed to depict the traffic dynamics involved in urban traffic systems. The link dynamics are described based on the cell-transmission model and bounded by the link capacities, while the flow dynamics are proposed…
A discrete and periodic complex Ginzburg-Landau equation, coupled to a discrete mean equation, is systematically derived from a driven and dissipative oscillator model, close to the onset of a supercritical Hopf bifurcation. The oscillator…
We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at…
This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works…
In this paper, we analyze the formation and dynamical properties of discrete light bullets (dLBs) in an array of passively mode-locked lasers coupled via evanescent fields in a ring geometry. Using a generic model based upon a system of…
We consider the ultradiscretization of a solvable one-dimensional chaotic map which arises from the duplication formula of the elliptic functions. It is shown that ultradiscrete limit of the map and its solution yield the tent map and its…
A system far from equilibrium is characterized by unconventional many-body dynamical effects, which can lead to anomalous density fluctuations and mass transport. Interestingly, these structural and dynamic features often emerge…
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are studied depending on two parameters. The system is…
Discrete max-linear Bayesian networks are directed graphical models specified by the same recursive structural equations as max-linear models but with discrete innovations. When all of the random variables in the model are binary, these…
Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in [22]. In this paper we continue to investigate this notion. In particular, we prove that all dynamical…
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
In this paper we research global dynamics and bifurcations of planar piecewise smooth quadratic quasi--homogeneous but non-homogeneous polynomial differential systems. We present sufficient and necessary conditions for the existence of a…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…