相关论文: The Lorenz model as a singularly perturbed nonline…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
We consider a class of nonlinear Schroedinger equation in three space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
It is well known that the Lorenz system has $Z_2$-symmetry. Using introducted in math.DS/0105147 topological covering-coloring a new representation for the Lorenz system is obtained. Deleting coloring leads to the factorized Lorenz system…
The influence of oscillatory perturbations on autonomous strongly nonlinear systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time, and their frequency increases according to a power law.…
It is found that Lorenz systems can be unidirectionally coupled such that the chaos expands from the drive system. This is true if the response system is not chaotic, but admits a global attractor, an equilibrium or a cycle. The extension…
We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap…
Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of…
Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle…
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes.
Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R^d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically…
The paper addresses the stabilization of nonlinear systems with semi-quadratic cost: quadratic with respect to controls and nonlinear for state variables. Paper presents the effective new feedback synthesis procedure. The novel feedback…
In the present paper it is analyzed a very simple example of pseudoextensive system, the tridimensional system of Linear Coupled Oscillators (OLA Model). The same one constitutes a classical tridimensional system of identical interacting…
In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems…
The Lorenz system is a milestone model of nonlinear dynamic systems. However, we report in this Letter that important information of the global solutions in the parameter space may still miss: there is a series of cascade solutions in…
Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are…
We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…
We interpret the Lorentz force equation as a geodesic equation associated with a non-linear connection. Using a geometric averaging procedure, we prove that for narrow and smooth one-particle distribution functions whose supports are…
Starting from the classical Saltzman 2D convection equations, we derive via a severe spectral truncation a minimal 10 ODE system which includes the thermal effect of viscous dissipation. Neglecting this process leads to a dynamical system…