Adaptive control of a four-dimensional memristor-based Chua's circuit

Main Article Content

Labed Boudjema
Mohammed Salah Abdelouahab


This paper investigates the behavior of a four-dimensional memristor-based Chua circuit. Specifically, we emphasize its chaotic and hyperchaotic behavior using the phase portrait and the Lyapunov spectrum. As chaos is deemed undesirable in numerous scientific disciplines, particularly in fields like robotics and electronic sciences, where the analyzed circuit holds potential applications in electronic device construction, we aim to alleviate such behaviors. To achieve this, we put forth an adaptive control strategy involving unknown parameters. The effectiveness of the suggested adaptive chaos control is established using the Lyapunov stability theory. To further illustrate and confirm our findings, we present numerical simulations, providing a visual representation of the successful application of the proposed adaptive control in managing the circuit's dynamics.



Download data is not yet available.


Metrics Loading ...

Article Details

How to Cite
Boudjema, L. and Abdelouahab, M.S. 2024. Adaptive control of a four-dimensional memristor-based Chua’s circuit. Journal of Innovative Applied Mathematics and Computational Sciences. 3, 2 (Jan. 2024), 190–202. DOI:
Research Articles
Author Biographies

Labed Boudjema, Department of Mathematics Mentouri University, Constantine 25017, Algeria




Mohammed Salah Abdelouahab, Laboratory of Mathematics and their Interactions, Abdelhafid Boussouf University Center, Mila 43000, Algeria




M. S. Abdelouahab, Les systèmes chaotiques à dérivées fractionnaires, PhD thesis, University of Constantine 1, Algeria, 2013.

A.H. Abolmasoumi and S. Khosravinejad, Chaos control in memristor-based oscillators using intelligent terminal sliding mode controller, International Journal of Computer Theory and Engineering, 8(6) (2016), 506–511.

B.C. Bao, Z. Liu and J.P. Xu, Transient chaos in smooth memristor oscillator, Chinese Physics B, 19(3) (2010). 030510.

B.C. Bao, J.P. Xu and Z. Liu,, Initial state dependent dynamical behaviors in memristor based chaotic circuit, Chinese Physics Letters, 27(7) (2010), 070504.

B.C. Bao, J.P. Xu, G.H. Zhou, and al, Chaotic memristive circuit: equivalent circuit realization and dynamical analysis, Chinese Physics B, 20(12) (2011), 120502.

N. Boudjerida, M. S. Abdelouahab, and R. Lozi, Modified projective synchronization of fractional-order hyperchaotic memristor-based Chuas circuit, Journal of Innovative Applied Mathematics and Computational Sciences, 2(3) (2022), 69–85.

N. Boudjerida, M. S. Abdelouahab, and R. Lozi, Nonlinear dynamics and hyperchaos in a modified memristor-based Chua’s circuit and its generalized discrete system, Journal of Difference Equations and Applications, (2023), 1–22.

L.O. Chua, Memristor: the missing circuit element, IEEE Transactions on Circuit Theory, 18(5) (1971), 507–519.

X. Huang, J. Jia, Y. Li and Z. Wang, Complex nonlinear dynamics in fractional and integer order memristor-based systems, Neurocomputing, (2016), 1–16.

M. Itoh and L.O. Chua, Memristor oscillators, International Journal of Bifurcation and Chaos, 18(11) (2008), 3183–3206.

S. Kaouache, M. S. Abdelouahab, Generalized synchronization between two chaotic fractional non-commensurate order systems with different dimensions, Nonlinear Dynamics and Systems Theory, 18(3) (2018), 273–284.

S. Kaouache, M. S. Abdelouahab, Inverse matrix projective synchronization of novel hyperchaotic system with hyperbolic sine function non-linearity, DCDIS B: Applications and Algorithms, 27 (2020), 145–154.

H.K. Khalil, Nonlinear Systems, Prentice Hall, New Jersey, USA, 2001.

B. Labed, S. Kaouache, and M. S. Abdelouahab, Control of a novel class of uncertain fractional-order hyperchaotic systems with external disturbances via sliding mode controller, Nonlinear Dynamics and Systems Theory, 20(2) (2020), 203–213.

Y. Li, X. Huang and M. Guo, The generation, analysis, and circuit implementation of a newmemristor based chaotic system, Mathematical Problems in Engineering, 2013.

Y. Li, X. Huang, Y. Song and J. Lin, A new fourth-order memristive chaotic system and its generation, International Journal of Bifurcation and Chaos, 25(11) (2015), 1550151.

B. Muthuswamy and P.P. Kokate, Memristor based chaotic circuits, IETE Technical Review, 26(6) (2009), 415–426.

D.B. Strukov, G.S. Snider, D.R. Stewart and R.S. Williams, The missing memristor found, Nature, 4534(1) (2008), 80–83.

S. Vaidyanathan, Chaos in neurons and adaptive control of Birkhoff-Shaw stange chaotic attractor, International Journal of PharmTech Research, 8(5) (2015), 956–963.

S. Vaidyanathan, Ch.K. Volos and V.T. Pham, Analysis, adaptive synchronization of a Nine-term novel 3-D chaotic system with four quadratic nonlinearities and its circuit simulation, Journal of engineering science and technology review, 8(2) (2015), 174–184.

M. Sun, L. Tian, Sh. Jiang and J. Xu, Feedback control and adaptive control of the energy resource chaotic system, ScienceDirect. Chaos, solitons and fractals 32(5) (2007), 1725–1734.

J. M. Yang and J.H. Kim, Sliding mode control for trajectory tracking of nonholonomic wheeled mobile Robots, IEEE Transaction on robotics and automatic, 15(3) (1999), 578–587.

S. Vaidyanathan, Sliding mode control of Rucklidge chaotic system for nonlinear double convection, International Journal of ChemTech Research, 8(8) (2015), 25–35.

S. Vaidyanathan, Global chaos synchronization of the Lotka-Volterra biological systems with four competitive species via active control, International Journal of PharmTech Research, 8(6) (2015), 206–217.

U. E. Vincent, Chaos synchronization using active control and backstepping control: A comparative analysis, Nonlinear Analysis: Modelling and Control, 13(2) (2008), 253–261.

U.E. Vincent and J.A. Laoye, Synchronization and control of directed transport in chaotic ratchets via active control, Science Direct. Physics Letters A 363 (2007), 91–95.

A. Wolf, J. Swift, H.L. Swinney and J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D: Nonlinear Phenomena, 16 (1985), 285–317.