Perturbations Of White Noise Type Research Articles

Capture into parametric autoresonance in the presence of noise

System of differential equations describing the initial stage of the capture of nonlinear oscillations into the parametric autoresonance is considered. Of special interest are resonant solutions whose amplitude increases without bound with time. The stability of such solutions ensures the physical observability of the autoresonant capture. We study the stability of such solutions with respect to persistent perturbations of white noise type, and we show that under certain restrictions on the intensity of the noise, the capture into parametric autoresonance is preserved with probability tending to one.

Multigroup deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delays: A stability analysis

In this paper, we investigate the dynamics of a multigroup disease propagation model with distributed delays and nonlinear incidence rates, which accounts for the relapse of recovered individuals. The main concern is the stability of the equilibria, sufficient conditions for global stability being obtained by applying Lyapunov‐LaSalle invariance principle and using Lyapunov functionals, which are constructed using their single‐group counterparts. The situation in which the deterministic model is subject to perturbations of white noise type is also investigated from a stability viewpoint.

Stochastic stability of a dynamical system perturbed by white noise

The effect of small constantly acting random perturbations of white noise type on a dynamical system with locally stable fixed point is studied. The perturbed system is considered in the form of Ito stochastic differential equations, and it is assumed that the perturbation does not vanish at a fixed point. In this case, the trajectories of the stochastic system issuing from points near the stable fixed point exit from the neighborhood of equilibrium with probability 1. Classes of perturbations such that the equilibrium of a deterministic system is stable in probability on an asymptotically large time interval are described.

Adaptive control of linear systems with coordinatewise-parametric perturbations of white noise type

Conditions for the mean-square dissipativity of adaptive stabilization systems for a linear object under coordinate-parametric perturbations of white noise type are obtained. A linear adaptive regulator with adjustable coefficients is chosen. For adjusting parameters, an adaptation algorithm is synthesized by the passification method. The number of inputs in objects under consideration may differ from that of outputs. The proof is based on the construction of a quadratic stochastic Lyapunov function. (In the case of purely parametric perturbations, the obtained conditions are known to be necessary and sufficient for the existence of a Lyapunov function with these properties.) Dissipativity conditions for the constructed closed system are obtained; it is shown that, in some special cases, the dissipativity of the closed system is preserved under white-noise perturbations of any intensity.

The destabilizing effect of parametric random perturbations of white noise type in certain quasilinear continuous dynamic systems

The destabilizing effect of parametric random perturbations of white noise type in certain quasilinear continuous dynamic systems

On the Phase Portrait of a Harmonic Oscillator with Friction Perturbed by a Random Process of White Noise Type

We study the phase portrait of a harmonic oscillator with friction for the case in which random perturbations of white noise type expressed in the Ito form act at a certain angle to the phase velocity vector.

Asymptotic analysis of nonlinear systems with small stochastic perturbations

By stochastic perturbations of white noise type, a nonlinear system will with probability 1 leave any bounded domain of state space that contains a stable equilibrium of the system. The escape time and its statistics are a measure for the stochastic stability of the system. Its statistical moments are found from the asymptotic solution of the singularly perturbed Fokker—Planck equation. For higher-dimensional systems, a numerical method has been developed for computing certain constants in the asymptotic solution of this equation. The method is applied to mechanical systems with stochastic input, stochastic population problems and to dynamical systems with multiple stable equilibria arising in hydrodynamics.