相关论文: The Lorenz model as a singularly perturbed nonline…

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…

Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…

Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…

A quasiparticle description of various condensed media is a very popular tool in study of their transport and thermodynamic properties. I present here a microscopic theory for the description of diffusion processes in two-component gas of…

We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…

We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…

A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…

We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr\"{o}dinger equation with the same type of the nonlinearity. The model opens a way to study the…

We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems…

In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic…

Stochastic resonance (SR) - a counter-intuitive phenomenon in which the signal due to a weak periodic force in a nonlinear system can be {\it enhanced} by the addition of external noise - is reviewed. A theoretical approach based on linear…

Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…

We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.

The quasi steady-state (QSS) model tries to reach a good compromise between accuracy and efficiency in long-term stability analysis. However, the QSS model is unable to provide correct approximations and stability assessment for the…

Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…

In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion…

We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…

A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…