The moment Lyapunov exponent of a co-dimension two bifurcation system driven by non-Gaussian colored noise

The Moment ◽

Abstract In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the stochastic dynamic equations with two degrees of freedom are established by piston theory and Galerkin approximate method. The fractional Kelvin–Voigt constitutive relation is used to describe the material properties of the viscoelastic plate, which leads to that the fractional derivation term is introduced into the stochastic dynamic equations. And the noise is simplified into an Ornstein-Uhlenbeck process by utilizing the path-integral method. Then, via the singular perturbation method, the approximate expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulations. Finally, the effects of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the viscoelastic plate are discussed.

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

Fluctuation and Noise Letters ◽

10.1142/s0219477518500104 ◽

2018 ◽

Vol 17 (02) ◽

pp. 1850010 ◽

Cited By ~ 1

Author(s):

D. L. Hu ◽

X. B. Liu

Keyword(s):

Lyapunov Exponent ◽

Stochastic Stability ◽

Colored Noise ◽

Singular Perturbation Method ◽

Random Forces ◽

Gaussian Colored Noise ◽

Path Integral Method ◽

The Moment ◽

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non–Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

Moment Lyapunov exponent and stochastic stability of binary airfoil driven by non-Gaussian colored noise

Nonlinear Dynamics ◽

10.1007/s11071-012-0577-x ◽

2012 ◽

Vol 70 (3) ◽

pp. 1847-1859 ◽

Cited By ~ 12

Author(s):

D. L. Hu ◽

Y. Huang ◽

X. B. Liu

Keyword(s):

Lyapunov Exponent ◽

Stochastic Stability ◽

Colored Noise ◽

Gaussian Colored Noise ◽

Moment Lyapunov Exponents of a Two-Dimensional Viscoelastic System Under Bounded Noise Excitation

Journal of Applied Mechanics ◽

10.1115/1.1445143 ◽

2002 ◽

Vol 69 (3) ◽

pp. 346-357 ◽

Cited By ~ 8

Author(s):

W.-C. Xie

Keyword(s):

Lyapunov Exponent ◽

Lyapunov Exponents ◽

Two Dimensional ◽

Bounded Noise ◽

Regular Perturbation ◽

Stochastic Fluctuation ◽

Viscoelastic System ◽

The Moment ◽

Moment Lyapunov Exponents

The moment Lyapunov exponents of a two-dimensional viscoelastic system under bounded noise excitation are studied in this paper. An example of this system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The stochastic parametric excitation is modeled as a bounded noise process, which is a realistic model of stochastic fluctuation in engineering applications. The moment Lyapunov exponent of the system is given by the eigenvalue of an eigenvalue problem. The method of regular perturbation is applied to obtain weak noise expansions of the moment Lyapunov exponent, Lyapunov exponent, and stability index in terms of the small fluctuation parameter. The results obtained are compared with those for which the effect of viscoelasticity is not considered.

Non-Gaussian Colored Noise Generation for Wireless Channel Simulation with Particle Swarm Optimizer

2020 14th European Conference on Antennas and Propagation (EuCAP) ◽

10.23919/eucap48036.2020.9135826 ◽

2020 ◽

Author(s):

Shaowei Dai ◽

Minghui Li ◽

Qammer H. Abbasi ◽

Muhammad Imran

Keyword(s):

Colored Noise ◽

Particle Swarm ◽

Wireless Channel ◽

Noise Generation ◽

Particle Swarm Optimizer ◽

Channel Simulation ◽

Gaussian Colored Noise ◽

First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2020.109767 ◽

2020 ◽

Vol 135 ◽

pp. 109767

Author(s):

Hongxia Zhang ◽

Wei Xu ◽

Qin Guo ◽

Ping Han ◽

Yan Qiao

Keyword(s):

Colored Noise ◽

Exit Time ◽

First Exit Time ◽

Escape Probability ◽

Gaussian Colored Noise ◽

THE ASYMPTOTIC BEHAVIOR OF SEMI-INVARIANTS FOR LINEAR STOCHASTIC SYSTEMS

Stochastics and Dynamics ◽

10.1142/s0219493702000388 ◽

2002 ◽

Vol 02 (02) ◽

pp. 281-294

Author(s):

G. N. MILSTEIN

Keyword(s):

Asymptotic Behavior ◽

Lyapunov Exponent ◽

Linear System ◽

Characteristic Function ◽

Stochastic Systems ◽

Random Variable ◽

Characteristic Functions ◽

Linear Stochastic Systems ◽

The Moment

The asymptotic behavior of semi-invariants of the random variable ln |X(t,x)|, where X(t,x) is a solution of a linear system of stochastic differential equations, is connected with the moment Lyapunov exponent g(p). Namely, it is obtained that the nth semi-invariant is asymptotically proportional to the time t with the coefficient of proportionality g(n)(0). The proof is based on the concept of analytic characteristic functions. It is also shown that the asymptotic behavior of the analytic characteristic function of ln |X(t,x)| in a neighborhood of the origin of the complex plane is controlled by the extension g(iz) of g(p).