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This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial…
The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of…
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the…
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian,…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths…
We consider a basic model of the lossless interaction between a moving two-level atom and a standing-wave single-mode laser field. Classical treatment of the translational atomic motion provides the semiclassical Hamilton-Schrodinger…