Complex nonlinear dynamics and vibration suppression of conceptual airfoil models: A state-of-the-art overview

Q Liu, Y Xu, J Kurths, X Liu - Chaos: An Interdisciplinary Journal of …, 2022 - pubs.aip.org
During the past few decades, several significant progresses have been made in exploring
complex nonlinear dynamics and vibration suppression of conceptual aeroelastic airfoil …

Responses of stochastic dynamical systems by the generalized cell mapping method with deep learning

X Yue, S Cui, B Pei, Y Xu - International Journal of Non-Linear Mechanics, 2022 - Elsevier
Experimental data is often corrupted by measurement noise in practical engineering and
there are multiple observed data under the same experimental condition. The noisy …

Averaging principle for distribution dependent stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

G Shen, J Xiang, JL Wu - Journal of Differential Equations, 2022 - Elsevier
In this paper, we study distribution dependent stochastic differential equations driven
simultaneously by fractional Brownian motion with Hurst index H> 1 2 and standard …

Averaging principle for stochastic differential equations with monotone condition

Z Guo, Y Xu, W Wang, J Hu - Applied Mathematics Letters, 2022 - Elsevier
In this paper, we consider the averaging principle for a class of stochastic differential
equations (SDEs) with the nonlinear terms only satisfying the local Lipschitz and monotone …

Stochastic averaging principle for distribution dependent stochastic differential equations

G Shen, J Song, JL Wu - Applied Mathematics Letters, 2022 - Elsevier
Due to the intrinsic link with (kinetic) nonlinear Fokker–Planck equations and many diverse
applications, distribution dependent stochastic differential equations have been investigated …

Two-time-scale stochastic differential delay equations driven by multiplicative fractional Brownian noise: Averaging principle

M Han, Y Xu, B Pei, JL Wu - Journal of Mathematical Analysis and …, 2022 - Elsevier
The main goal of this article is to study an averaging principle for a class of two-time-scale
stochastic differential delay equations in which the slow-varying process includes a …

Optimal index and averaging principle for Itô–Doob stochastic fractional differential equations

W Wang, Z Guo - Stochastics and Dynamics, 2022 - World Scientific
In this paper, a class of Itô–Doob stochastic fractional differential equations (Itô–Doob
SFDEs) models are discussed. Using the time scale transformation method, we consider the …

Averaging principle for a class of time-fractal-fractional stochastic differential equations

X Xia, Y Chen, L Yan - Fractal and Fractional, 2022 - mdpi.com
In this paper, we study a class of time-fractal-fractional stochastic differential equations with
the fractal–fractional differential operator of Atangana under the meaning of Caputo and with …

Stochastic averaging for a type of fractional differential equations with multiplicative fractional Brownian motion

R Wang, Y Xu, B Pei - Chaos: An Interdisciplinary Journal of Nonlinear …, 2022 - pubs.aip.org
This paper focuses on the averaging principle of Caputo fractional stochastic differential
equations (SDEs) with multiplicative fractional Brownian motion (fBm), where Hurst …

Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients

R Wang, Y Xu, H Yue - Statistics & Probability Letters, 2022 - Elsevier
This paper investigates a non-autonomous slow–fast system, which is generalized by
stochastic differential equations with locally Lipschitz coefficients, subjected to standard …