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

• Published in: Journal of low frequency noise, vibration, and active control Vol. 38; no. 3-4; pp. 1279 - 1296
• Main Authors: Khan, Najeeb A, Hameed, Tooba, Razzaq, Oyoon A, Ayaz, Muhammad
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.12.2019; Sage Publications Ltd; SAGE Publishing
• Subjects: Artificial neural networks; Bifurcations; Chaos theory; Computer simulation; Error analysis; Laplace transforms; Neural networks; Runge-Kutta method; Scrolling; Simulated annealing; Simulation; Wavelet analysis; bifurcation analysis; chaotic dynamics; Chua’s system; Fractional calculus
• ISSN: 1461-3484; 2048-4046
• DOI: 10.1177/1461348418813015

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.