Tracking the chaotic behaviour of fractional-order Chua’s system by Mexican hat wavelet-based artificial neural network

In this paper, a process is devised systematically to scrutinize the scrolling chaotic behaviour of fractional-order Chua's system. The process is composed of fractional Laplace transformation, artificial neural network with Mexican hat wavelet as an activation function and simulated annealing....

Full description

Saved in:
Bibliographic Details
Published in:Journal of low frequency noise, vibration, and active control vibration, and active control, 2019-12, Vol.38 (3-4), p.1279-1296
Main Authors: Khan, Najeeb A, Hameed, Tooba, Razzaq, Oyoon A, Ayaz, Muhammad
Format: Article
Language:English
Subjects:
Artificial neural networks
Bifurcations
Chaos theory
Computer simulation
Error analysis
Laplace transforms
Neural networks
Runge-Kutta method
Scrolling
Simulated annealing
Simulation
Wavelet analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, a process is devised systematically to scrutinize the scrolling chaotic behaviour of fractional-order Chua's system. The process is composed of fractional Laplace transformation, artificial neural network with Mexican hat wavelet as an activation function and simulated annealing. Sequentially, the parametric expansion of fractional Laplace transform is employed to convert the governing fractional system into an ordinary differential system. Next, artificial neural network and simulated annealing approximate and optimize the attained system and produce accurate solutions. The predictability and elaboration of double scrolling chaotic structures of fractional-order Chua's system are also studied using the Lyapunov exponent and fifth–fourth Runge–Kutta method. Moreover, the mean absolute error and root mean square error are measured for the convergence analysis of the proposed scheme. On the whole, the accurate approximate solutions, the phase plots of Lyapunov exponent spectrum and bifurcation maps of the dynamical evolution of fractional Chua's system are a triumph of this endeavour.
ISSN:1461-3484
2048-4046
DOI:10.1177/1461348418813015