Related papers: Lyapunov Potential Description for Laser Dynamics
We analyze the motion of an overdamped classical particle in a multidimensional periodic potential, driven by a weak external noise. We demonstrate that in steady-state, the presence of temporal correlations in the noise and spatial…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
Non Born-Oppenheimer quantum dynamics of H$_{2}^{+}$ excited by shaped one-cycle laser pulses linearly polarized along the molecular axis have been studied by the numerical solution of the time-dependent Schr\"odinger equation within a…
We consider a generalization of the classical nonrelativistic St\"{o}rmer problem, describing the motion of charged particles in a purely magnetic dipole field, by taking into account the effects of the dissipation, assumed to be of…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as…
Multimode intracavity frequency-doubled lasers can reach states of amplitude noise suppression orders of magnitude beyond the predictions of independent-mode partition statistics. We show that the chi2 coupled-wave dynamics in the doubling…
The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…
Recently, stochastic resonance was obtained numerically in an underdamped periodic potential system driven by a periodic force and a Gaussian white noise. In that numerical work, the occurrence of stochastic resonance was explained in terms…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
Analytic potentials are built for all four $^{2S+1}\Pi_{u/g}$ states of Li$_{2}$ dissociating to Li$(2S)$ + Li$(3P)$: $3b(3^{3}\Pi_{u})$, $3B(3^{1}\Pi_{u})$, $3C(3^{1}\Pi_{g}),$ and $3d(3^{3}\Pi_{g})$. These potentials include the effect of…
For a Markov and stationary stochastic process described by the well-known classical master equation, we introduce complex transition rates instead of real transition rates to study the pre-thermal oscillatory behaviour in complex…
An analytical expression for the maximal Lyapunov exponent $\lambda_1$ in generalized Fermi-Pasta-Ulam oscillator chains is obtained. The derivation is based on the calculation of modulational instability growth rates for some unstable…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
Harmonic mode-locking, realized actively or passively, is an effective technique for increasing the repetition rate of lasers, with important applications in optical sampling, laser micro-machining and frequency metrology. It is critically…
We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results in this direction, which hold for potentials satisfying…
The cyclic motion of particles in a periodic potential under the influence of a constant external force is analyzed in an atom optical approach based on Landau-Zener transitions between two resonant states. The resulting complex picture of…
Pulsating behavior is a universal phenomenon in versatile fields. In nonlinear dissipative systems, the solitons could also pulsate under proper conditions and show many interesting dynamics. However, the pulsation dynamics is generally…
We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials.…
The dynamics of two-level systems in an external periodic field are investigated in general. The necessary conditions of localization are obtained through analysing the time-evolving matrix. It is found that localization is possible if not…