Related papers: Relaxation time in a non-conserving driven-diffusi…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
We investigate the dynamics of a two-mode laser system by extending the two-mode Tavis-Cummings model with dissipative channels and incoherent pumping and by applying the mean-field approximation in the thermodynamic limit. To this end we…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Recently it is shown that there are three families of stochastic one-dimensional non-equilibrium lattice models for which the single-shock measures form an invariant subspace of the states of these models. Here, both the stationary states…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a $1+1$-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is…
We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
Nonlinear systems, such as switching DC-DC boost or buck converters, have rich dynamics. A simple one-dimensional discrete-time model is used to analyze the boost or buck converter in discontinuous conduction mode. Seven different control…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation. In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We propose a generalized parity-time ($\mathcal{PT}$) -symmetric Li\'enard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of…
The paper addresses the problem of relaxation of open quantum systems. Using the path integral methods we found an analytical expression for time-dependent density matrix of two coupled quantum oscillators interacting with different baths…
We study the evolution of a two-state system that is monitored continuously but with interactions with the detector tuned so as to avoid the Zeno affect. The system is allowed to interact with a sequence of prepared probes. The…