Research on Stochastic Resonance of Fractional-Order Coupled System Excited by Trichotomous Noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
◽  
Keyword(s):  
Stochastic Resonance ◽  
Fractional Order ◽  
Coupled System ◽  
Trichotomous Noise

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag–Leffler Kernel

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
P. Veeresha ◽  
D. G. Prakasha ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Coupled System ◽  
Order Model ◽  
Science And Engineering ◽  
Transform Method ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis

Abstract In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method (q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag–Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.

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