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Adaptive Control and Circuit Implementation of a New 3-Dimensional Chaotic System with Quadratic, Cubic and Quartic Nonlinearities


Babatunde A. Idowu, K. S. Oyeleke, Olasunkanmi I. Olusola, Sundarapandian Vaidyanathan, Aceng Sambas, MohamadAfendee Mohamed, Mustafa Mamat, Sukono
Abstract

In this article, a new 3-D chaotic system with three nonlinearities is put forward. The new system which was achieved by modifying the Vaidyanathan chaotic system (2019) consists of a quadratic nonlinearity, cubic nonlinearity and quartic nonlinearity. The phase portraits, dynamical analysis, Kaplan-Yorke fractal dimension ( = 2.2251), Lyapunov exponents ( = 1.1695,  = 0 and  = −5.1695) and so on are derived for the new chaotic system. We utilized the adaptive control theory to achieve control of the new system and also global synchronization of two of the identical new chaotic systems with unknown parameters. Numerical simulations were implemented to achieve the adaptive synchronization results. An electronic circuit model of the new chaotic system was designed using MultiSim. The MultiSim outputs of the new chaotic system show good match with the MATLAB phase plots of the new chaotic system. The MultiSim electronic design of the new chaotic system is useful for applications in engineering

Volume 12 | Issue 6

Pages: 792-806

DOI: 10.5373/JARDCS/V12I6/S20201095