AUTHORS: Aceng Sambas, Mustafa Mamat, Sundarapandian Vaidyanathan, Mohamad Afendee Mohamed, W. S. Mada Sanjaya, Mujiarto

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ABSTRACT: A 3-D novel hidden chaotic attractor with no equilibrium point is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. As an engineering application, adaptive synchronization of identical hidden chaotic attractors with no equilibrium point is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the novel hidden chaotic attractor is presented in detail to confirm the feasibility of the theoretical hidden chaotic attractor model. The outputs show that results of the system modelled in MATLAB simulation confirm the MultiSIM results.

KEYWORDS: - Chaos, hidden attractor, synchronization, numerical simulation, circuit design.

REFERENCES:

[1]. A. T. Azar, and S. Vaidyanathan, modeling and control systems design Germany: Springer, 2015.

[2]. A. T. Azar, and S. Vaidyanathan, chaos theory and intelligent control Germany: Springer, 2016.

[3]. B. C. Bao, P. Y. Wu, H. Bao, Chen. Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in thirdmemristive oscillator. Chaos, Solitons & Fractals, Vol. 106, 2018, pp.

[4]. S. Mishra and R. D. S. Yadava Chaotic Self-Modulation in Nonlinear Colpitts Oscillator and its Potential Applications. Circuits, Systems, and Signal Processing, Vol. 37, No. 2, 2018,

[5]. A. Sambas, S. Vaidyanathan, M. Mamat, W. S. M. Sanjaya, R. P. Prastio. Design, analysis of the Genesio-Tesi chaotic system and its electronic experimental implementation. International Journal of Control Theory and Applications, Vol. 9, No. 1, 2016, pp. 141

[6]. V. K.Yadav, S. Das, B. S. Singh and M. Srivastava. chaos control of a fractional order chaotic chemical reactor system and its function projective synchronization with parametric uncertainties. Chinese Journal of Physics 55, No. 3, 2017, pp. 594-605.

[7]. S. Vaidyanathan, Adaptive control of a chemical chaotic reactor. Int J PharmTech Res, Vol. 8, No. 3, 2015, pp. 377-382.

[8]. K. Usha, P. A. Subha, and C. R. Nayak. The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network. Chaos, Solitons & Fractals, Vol. 108, 2018, pp. 25-31.

[9]. E. C. Massoud, J. Huisman, E. Benincà, M. C. Dietze, W. Bouten, and J. A. Vrugt. Probing the limits of predictability: data assimilation of chaotic dynamics in complex food webs. Ecology letters, Vol. 21, No. 1, 2018, pp. 93-103.

[10]. G. Cai and J. Huang. A new finance chaotic attractor. International Journal of Nonlinear Science, Vol. 3, No. 3, 2007, pp. 213-220.

[11]. A Sambas, S. Vaidyanathan, M. Mamat, W. S. M. Sanjaya and D. S. Rahayu. A 3-D novel jerk chaotic system and its application in secure communication system and mobile robot navigation. Studies in Computational Intelligence, Vol. 636, 2016, pp. 283-310.

[12]. S. Vaidyanathan, A. Sambas, M. Mamat and W. S. M. Sanjaya A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot. Archives of Control Sciences, Vol. 27, No. 4, 2017, pp. 541-554.

[13]. R. Ebrahimi, M. Ghayour and H. M. Khanlo. Chaotic vibration analysis of a coaxial rotor system in active magnetic bearings and contact with auxiliary bearings. Journal of Computational and Nonlinear Dynamics, Vol. 12, No. 3, 2017, Article ID 031012.

[14]. C. M. Marinho, E. E. Macau, and T. Yoneyama Chaos over chaos: A new approach for satellite communication. Acta Astronautica, Vol. 57, No. 2, 2005, pp. 230-238.

[15]. J. Zhang and X. Liao. Synchronization and chaos in coupled memristor-based FitzHughNagumo circuits with memristor synapse. AEU-International Journal of Electronics and Communications, Vol. 75, 2017, pp. 82-90.

[16]. S. Vaidyanathan and Ch. K. Volos. Advances in memristors, memristive devices and systems. Germany: Springer, 2017.

[17]. S. Vaidyanathan, A. Sambas M. Mamat and W. S. M. Sanjaya. Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption. International Journal of Modelling, Identification and Control, Vol. 28, No. 2, 2017, pp. 153-166.

[18]. A. Sambas, W. S. M. Sanjaya and M. Mamat,. Design and numerical simulation of unidirectional chaotic synchronization and its application in secure communication system. Journal of Engineering Science and Technology Review, Vol. 6, No. 4, pp. 66-73.

[19]. A. Sambas, M. Mamat, W. S. M. Sanjaya, Z. Salleh and F. S. Mohamad. Secure communications based on the synchronization of the new Lorenz-like attractor circuit. Advanced Studies in Theoretical Physics, Vol. 9, No. 8, 2015, pp. 379-394.

[20]. B. Vaseghi, M. A. Pourmina and S. Mobayen. Secure communication in wireless sensor networks based on chaos synchronization using adaptive sliding mode control. Nonlinear Dynamics, Vol. 89, No. 3, 2017, pp. 1689- 1704.

[21]. T. Gotthans and J. Petržela. New class of chaotic systems with circular equilibrium. Nonlinear Dynamics, Vol. 81, No. 3, 2015, pp. 1143-1149.

[22]. T. Gotthans, J. C. Sprott, and J. Petrzela. Simple chaotic flow with circle and square equilibrium. International Journal of Bifurcation and Chaos, Vol. 26, No. 8, 2016, Article ID 1650137.

[23]. V. T. Pham, S. Jafari, X. Wang, and J. Ma. A chaotic system with different shapes of equilibria. International Journal of Bifurcation and Chaos, Vol. 26, No. 4, 2016, Article ID 1650069.

[24]. V. T. Pham, S. Jafari, Ch. K. Volos, A. Giakoumis, S. Vaidyanathan and T. Kapitaniak. A chaotic system with equilibria located on the rounded square loop and its circuit implementation. IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 63, No. 9, 2016, pp. 878-882.

[25]. S. Jafari, and J. C. Sprott. Simple chaotic flows with a line equilibrium. Chaos, Solitons & Fractals, Vol. 57, 2013, pp. 79-84.

[26]. V. T. Pham, S. Jafari, and Ch. K. Volos. A novel chaotic system with heart-shaped equilibrium and its circuital implementation. Optik-International Journal for Light and Electron Optics, Vol. 131, 2017, pp. 343-349.

[27]. J. Petrzela and T. Gotthans. New chaotic dynamical system with a conic-shaped equilibrium located on the plane structure. Applied Sciences, Vol. 7, No. 10, 2017, Article ID 976.

[28]. S. Mobayen, Ch. K. Volos, S. Kaçar, and U. Çavuşoğlu. New class of chaotic systems with equilibrium points like a three-leaved clover. Nonlinear Dynamics, Vol. 91, No. 2, 2018, pp. 939-956.

[29]. A. Sambas, S. Vaidyanathan, M. Mamat, and W. S. M. Sanjaya. A Six-Term Novel Chaotic System with Hidden Attractor and Its Circuit Design. Studies in Systems, Decision and Control. Vol. 133, 2018, pp. 365-373.

[30]. S. Vaidyanathan, V. T. Pham, Ch. K. Volos and A. Sambas. A Novel 4-D Hyperchaotic Rikitake Dynamo System with Hidden Attractor, its Properties, Synchronization and Circuit Design. Studies in Systems, Decision and Control. Vol. 133, 2018, pp. 345-364.

[31]. S. Jafari, J. C. Sprott and S. M. R. H. Golpayegani. Elementary quadratic chaotic flows with no equilibria. Physics Letters A, Vol. 377, No. 9, 2013, pp. 699-702.

[32]. C. Li, W. Hu, J. C. Sprott, and X. Wang. Multistability in symmetric chaotic systems. The European Physical Journal Special Topics, Vol. 224, No. 8, 2015, pp. 1493-1506.

[33]. C. Li and J. C. Sprott. Coexisting hidden attractors in a 4-D simplified Lorenz system. International Journal of Bifurcation and Chaos, Vol. 24, No. 3, 2014, Article ID 1450034.

[34]. G. A. Leonov, N. V. Kuznetsov and T. Mokaev. Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity. Communications in Nonlinear Science and Numerical Simulation, Vol. 28, No. 1, 2015, pp. 166-174.

[35]. G. A. Leonov, N. V. Kuznetsov, M. A. Kiseleva, E. P. Solovyeva, and A. M. Zaretskiy. Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor. Nonlinear Dynamics, Vol. 77, No. 1, 2014, pp. 277-288.

[36]. H. K. Khalil, Nonlinear Systems. New York: Prentice Hall, 2002.