An optimal nonlinear control for anti-synchronization of Rabinovich hyperchaotic system

Shaymaa Al-hayali, Saad Fawzi AL-Azzawi


This work derives new results for the anti-synchronization of 4D identical Rabinovich hyperchaotic systems by using two strategies: active and nonlinear control. The stabilization results of error dynamics systems are established based on Lyapunov second method. Control is designed via the relevant variables of drive and response systems.  In comparison with previous strategies, the current controller (Nonlinear control) focused on the minimum possible limits for relevant variables. The better performance is realizing the anti- synchronization by designing a control with low terms. After obtaining analytical results of the proposed controller, numircal simulation is carried out using Matlab. The graphical results prove validity and applicability of proposed control without know any parameter.The proposed control has certain significance for reducing the time and complexity for strategy implementation.


Anti- synchronzition, active control, nonlinear control, Lyapunov second method.


AL-Azzawi. S.F. Stability and bifurcation of pan chaotic system by using Routh-Hurwitz and Gardan method. Appl. Math. Comput. (2012) 219: 1144-1152.

Chen. HK. Global Chaos synchronization of newchaotic systems via nonlinear control. Chaos, Solitons and Fractals. (2005) 23: 1245-1251.

Al-Obeidi. A. S., AL-Azzawi. S. F. Complete synchronization of a novel 6-D hyperchaotic Lorenz system with known parameters. International Journal of Engineering & Technology. (2018),7(4): 5345-5349.

Wei Z., Sang B., L. Universtiy, and W. Zhang, “Complex Dynamical Behaviors in a 3D Simple Chaotic Flow with 3D Stable or 3D Unstable Manifolds of a Single Equilibrium. International Journal of Bifurcation and Chaos (2019) 29(7):1950095-1950110.

Al-Obeidi. A. S., AL-Azzawi. S. F. Chaos synchronization of a class 6-D hyperchaotic Lorenz system. Modelling, Measurement and Control B. (2019),88(1):17-22.

Park. J. H. Chaos synchronization of a chaotic system via nonlinear control. Chaos Solitons Fractals. (2005)25: 579-584.

Aziz. M. M., AL-Azzawi. S. F. Anti-synchronization of nonlinear dynamical systems based on Cardano’s method. Optik. (2017) 134: 109–120.

Al-Obeidi. A. S. AL-Azzawi. S. F. Projective synchronization for a class of 6-D hyperchaotic Lorenz system. Indonesian Journal of Electrical Engineering and Computer Science. (2019)16(2):692-700.

Cai G. and Tan Z., “Chaos synchronization of a new chaotic system via nonlinear control” Journal of Uncertain Systems (2007) 1(3): 235–240.

Aziz. M. M., AL-Azzawi. S. F. Hybrid chaos synchronization between two different hyperchaotic systems via two approaches. Optik. (2017) 138: 328–340.

Jia. Q. Hyperchaos synchronization between two different hyperchaotic systems. Journal of Information and Computing Science. (2008).3: 73–80.

Lu. D., Wang. A., Tian. X. Control and synchronization of a new hyperchaotic system with unknown parameters. International Journal of Nonlinear Science. (2008) 6: 224-229.

Aziz. M. M., AL-Azzawi. S. F. Some Problems of feedback control strategies and its treatment. Journal of Mathematics Research. (2017) 9(1): 39-49.

AL-Azzawi S.F. and Aziz M.M. Chaos synchronization of nonlinear dynamical systems via a novel analytical approach, Alexandria Engineering Journal, (2018) 57(4): 3493–3500

AL-Azzawi S.F. and Aziz M.M., Strategies of linear feedback control and its classification, Telkomnika, (2019)17(4):1931-1940.

Yang. Q., Osman. W. M., Chen. C. (2015). A new 6D hyperchaotic system with four positive Lyapunov exponents coined. International Journal of Bifurcation and Chaos. (2015) 25(4):1550061–1550079

A. Sambas, M. Mamat, A. A. Arafa, G. M. Mahmoud, M. A. Mohamed and W. S. M. Sanjaya. “A new chaotic system with line of equilibria: dynamics, passive control and circuit design,” International Journal of Electrical and Computer Engineering, (2019) 9(4):2365-2376.

S. Mobayen, S. Vaidyanathan, A. Sambas, S. Kaar and U. Cavusoglu. “A novel chaotic system with boomerang-shaped equilibrium, its circuit implementation and application to sound encryption,” Iranian Journal of Science and Technology, Transactions of Electrical Engineering, (2019) 43(1): 1-12.

Sambas A., Vaidyanathan S., Mamat M., Mohamed M. A. and Sanjaya W. S.M“A new chaotic system with a pear-shaped equilibrium and its circuit simulation,” International Journal of Electrical and Computer Engineering, 2018. 8(6): 4951-4958,

Vaidyanathan S., Sambas A., and Mamat M. “A new chaotic system with axe-shaped equilibrium, its circuit implementation and adaptive synchronization,” Archives of Control Sciences, (2018) 28(3), 443- 462.

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