Search results for "Linear dynamical system"

Non-linear systems under parametric a-stable Levý white noises

2005

Vehicular Motion and Traffic Breakdown: Evaluation of Energy Balance

2009

Microscopic traffic models based on follow–the–leader behaviour are strongly asymmetrically interacting many–particle systems. The well–known Bando’s optimal velocity model includes the fact that (firstly) the driver is always looking forward interacting with the lead vehicle and (secondly) the car travels on the road always with friction. Due to these realistic assumptions the moving car needs petrol for the engine to compensate dissipation by rolling friction. We investigate the flux of mechanical energy to evaluate the energy balance out of the given nonlinear dynamical system of vehicular particles. In order to understand the traffic breakdown as transition from free flow to congested t…

Robust regulation with an H<inf>∞</inf> constrain for linear two-time scale systems

2010

In this paper, the problem of robust multi-objective control design with an H ∞ constrain is studied for a class of linear two-time scale systems. The design is based on a new modelling approach under the assumption of norm-boundedness of the fast dynamics. In this method, a portion of the fast dynamics is treated as a norm-bounded perturbation in the design by its maximum possible gain. In this view, the problem of robust multi-objective control design is performed only for the certain dynamics of the two-time scale system, whose order is less than that of the original system. One illustrative example is used to demonstrate the validity of the proposed approach.

Moment Equations for a Spatially Extended System of Two Competing Species

2005

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulat…

Attracteur de polarisation dans les fibres optiques

2004

Nous etudions la dynamique non lineaire des etats de polarisation de deux ondes coherentes ou incoherentes se propageant dans une fibre optique. Nous presentons en particulier un effet original d'attraction de la polarisation.

Noise delayed decay of unstable states: theory versus numerical simulations

2004

We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for polynomial potential profiles and obtain nonmonotonic behavior of the decay times as a function of the noise intensity for the unstable nonequilibrium states. The analytical results are compared with numerical simulations.

Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures

1987

This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton-Jacobi theory and other problems such as the definition and globalization of the Poincare-Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different…

Asymptotic properties of incoherent waves propagating in an all-optical regenerators line

2007

International audience; We present an original method to generate optical pulse trains with random time-interval values from incoherent broadband sources. More precisely, our technique relies on the remarkable properties of a line made of cascaded self-phase modulation-based optical regenerators. Depending on the regenerator parameters, various regimes with noticeably different physical behaviors can be reported.

Attractors for non-autonomous retarded lattice dynamical systems

2015

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Experimental and numerical enhancement of Vibrational Resonance in a neural circuit

2012

International audience; A neural circuit exactly ruled by the FitzHugh-Nagumo equations is excited by a biharmonic signal of frequencies f and F with respective amplitudes A and B. The magnitude spectrum of the circuit response is estimated at the low frequency driving f and presents a resonant behaviour versus the amplitude B of the high frequency. For the first time, it is shown experimentally that this Vibrational Resonance effect is much more pronounced when the two frequencies are multiple. This novel enhancement is also confirmed by numerical predictions. Applications of this nonlinear effect to the detection of weak stimuli are finally discussed.