Related papers: Sensitivity to Cumulative Perturbations for a Clas…
We investigate sensitivity to cumulative perturbations for a few dynamical system classes of practical interest. A system is said to have bounded sensitivity to cumulative perturbations (bounded sensitivity, for short) if an additive…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
Hybrid systems are dynamical systems with continuous-time and discrete-time components in their dynamics. When hybrid systems are defined on a principal bundle we are able to define two classes of impacts for the discrete-time transition of…
We present results from an individual particle based model for the collision, coagulation and fragmentation of heavy drops moving in a turbulent flow. Such a model framework can help to bridge the gap between the full hydrodynamic…
Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models,…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
The defining feature of chaos is its hypersensitivity to small perturbations. However, we report a stability of branched flow against large perturbations where the classical trajectories are chaotic, showing that strong perturbations are…
The dissipation effect in a hybrid system is studied in this Letter. The hybrid system is a compound of a classical magnetic particle and a quantum single spin. Two cases are considered. In the first case, we investigate the effect of the…
In this article, we demonstrate that in a transport model of particles with kinetic constraints, long-lived spatial structures are responsible for the blocking dynamics and the decrease of the current at strong driving field. Coexistence…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from…
Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness"…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
In this paper, we study the probabilistic stability analysis of a subclass of stochastic hybrid systems, called the Planar Probabilistic Piecewise Constant Derivative Systems (Planar PPCD), where the continuous dynamics is deterministic,…
We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two…
This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector…
We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…