A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation
-
2018-08-24 https://doi.org/10.14419/ijet.v7i3.14865 -
Chaos, chaotic systems, circuit simulation, four-scroll system, Lyapunov exponents -
Abstract
This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.
-
References
[1] E.H. Hellen and E. Volkov, “How to couple identical ring oscillators to get quasiperiodicity, extended chaos, multistability, and the loss of symmetryâ€, Communications in Nonlinear Science and Numerical Simulation, Vol. 62, (2018), pp. 462–479.
[2] L.Wang and X.S. Yang, “Global analysis of a generalized Nose-Hoover oscillatorâ€, Journal of Mathematical Analysis and Applications, Vol. 464, No. 1, (2018), pp. 370–379.
[3] S. Vaidyanathan and S. Rasappan, “Hybrid synchronization of hyperchaotic Qi and L¨u systems by nonlinear controlâ€, Communications in Computer and Information Science, Vol. 131, (2011), pp. 585–593.
[4] V.T. Pham, C.K. Volos and S. Vaidyanathan, “Multi-scroll chaotic oscillator based on a first-order delay differential equationâ€, Studies in Computational Intelligence, Vol. 581, (2015), pp. 59–72.
[5] S. Vaidyanathan, C.K. Volos and V.T. Pham, “Global chaos control of a novel nine-term chaotic system via sliding mode controlâ€, Studies in Computational Intelligence, Vol. 576, (2015), pp. 571–590.
[6] D. Ghosh, A. Mukherjee, N.R. Das and B.N. Biswas, “Generation & control of chaos in a single loop optoelectronic oscillatorâ€, Optik, Vol.165, (2018), pp. 275–287.
[7] S. Vaidyanathan, “Output regulation of the forced Van der Pol chaotic oscillator via adaptive control methodâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 106–116.
[8] S. Vaidyanathan, “Global chaos synchronization of the forced Van der Pol chaotic oscillators via adaptive control methodâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 156–166.
[9] O.I. Massoud, J. Huisman, E. Beninca, M.C. Dietze, W. Bouten, and J.A. Vrugt, “Probing the limits of predictability: data assimilation of chaotic dynamics in complex food websâ€, Ecology Letters, Vol. 21, No. 1, (2018), pp. 93–103.
[10] S. Vaidyanathan, ‘Lotka-Volterra population biology models with negative feedback and their ecological monitoringâ€, International Journal of PharmTech Research, Vol. 8, No. 5, (2015), pp. 974–981.
[11] J.C. Sprott, J.A. Vano, J.C. Wildenberg, M.B. Anderson, J.K. Noel, “Coexistence and chaos in complex ecologiesâ€, Physics Letters A, Vol. 335, No. 2–3, (2005), pp. 207–212.
[12] S. Panahi, Z. Aram, S. Jafari, J. Ma and J.C. Sprott, “Modeling of epilepsy based on chaotic artificial neural networkâ€, Chaos, Solitons and Fractals, Vol. 105, (2017), pp. 150–156.
[13] I. Bashkirtseva, V. Nasyrova and L. Ryashko, “Noise-induced bursting and chaos in the two-dimensional Rulkov modelâ€, Chaos, Solitons and Fractals, Vol. 110, (2018), pp. 76–81.
[14] J. Guckenheimer and R.A. Oliva, “Chaos in the Hodgkio-Hoxley modelâ€, SIAM Journal on Applied Dynamical Systems, Vol. 1, No. 1, (2002), pp. 105–114.
[15] S. Vaidyanathan, “Adaptive control of the FitzHugh-Nagumo chaotic neuron modelâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 117–127.
[16] Y. Yang, X. Liao and T. Dong, “Period-adding bifurcation and chaos in a hybrid Hindmarsh-Rose modelâ€, Neural Networks, Vol. 105, (2018), pp. 26–35.
[17] M. Kim, U. Ha, K.J. Lee, Y. Lee, and H.J. Yoo, “A 82-nW Chaotic Map True Random Number Generator Based on a Sub-Ranging SAR ADCâ€, IEEE Journal of Solid-State Circuits, Vol. 52, No. 7, (2017), pp. 1953–1965.
[18] K. Bouallegue, “A new class of neural networks and its applicationsâ€, Neurocomputing, Vol. 249, (2017), pp. 28–47.
[19] S. Vaidyanathan, “Synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control methodâ€, International Journal of PharmTech Research, Vol. 8, No. 5, (2015), pp. 946–955.
[20] M. Sadeghpour, M. Khodabakhsh and H. Salarieh, “Intelligent control of chaos using linear feedback controller and neural network identifierâ€, Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 12, (2012), pp. 4731–4739.
[21] Y. Dai, H. Wang, and H. Sun, “Cyclic-shift chaotic medical image encryption algorithm based on plain text key-streamâ€, International Journal of Simulation: Systems, Science and Technology, Vol. 17, No. 27, (2016), pp. 24.1-24.8.
[22] A. Ullah, S. S. Jamal and T. Shah, “A novel scheme for image encryption using substitution box and chaotic systemâ€, Nonlinear Dynamics, Vol. 91, No. 1, (2018), pp. 359-370.
[23] N.K. Pareek, V. Patidar and K.K. Sud, “Image encryption using chaotic logistic mapâ€, Image and Vision Computing, Vol. 24, No. 9, (2006), pp. 926–934.
[24] A.A. Elsadany, A.M. Yousef and A. Elsonbaty, “Further analytical bifurcation analysis and applications of coupled logistic mapsâ€, Applied Mathematics and Computation, Vol. 338, (2018), pp. 314–336.
[25] 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 encryptionâ€, International Journal of Modelling, Identification and Control, Vol. 28, No. 2, (2017), pp.153-166.
[26] O.I. Tacha, Ch. K. Volos, I.M. Kyprianidis, I.N. Stouboulos, S. Vaidyanathan and V. T. Pham, “Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemâ€, Applied Mathematics and Computation, Vol. 276, (2016), pp. 200–217.
[27] I. Klioutchnikov, M. Sigova and N. Beizerov, “Chaos theory in Financeâ€, Procedia Computer Science, Vol. 119, (2017), pp. 368–375.
[28] M.O. Fen, “Persistence of chaos in coupled Lorenz systemsâ€, Chaos, Solitons & Fractals, Vol. 95, (2017), pp. 200–205.
[29] S. Rasappan and S. Vaidyanathan, “Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping controlâ€, Far East Journal of Mathematical Sciences, Vol. 67, No. 2, (2012), pp. 265–287.
[30] S. Vaidyanathan, C.K. Volos, K. Rajagopal, I.M. Kyprianidis and I.N. Stouboulos, “Adaptive backstepping controller design for the antisynchronization of identical WINDMI chaotic systems with unknown parameters and its SPICE implementationâ€, Journal of Engineering Science and Technology Review, Vol. 8, No. 2, (2015), pp. 74–82.
[31] S. Vaidyanathan, “Adaptive synchronization of novel 3-D chemical chaotic reactor systemsâ€, International Journal of ChemTech Research, Vol. 8, No. 7, (2015), pp. 159–171.
[32] S. Sarwar and S. Iqbal, “Stability analysis, dynamical behavior and analytical solutions of nonlinear fractional differential system arising in chemical reactionâ€, Chinese Journal of Physics, Vol. 56, No. 1, (2018), pp. 374–384.
[33] C. Xu and Y. Wu, “Bifurcation and control of chaos in a chemical systemâ€, Applied Mathematical Modelling, Vol. 39, No. 8, (2015), pp. 2295–2310.
[34] I. Dodale and V.A. Oancea, “Chaos control for Willamowski-Rossler model of chemical reactionsâ€, Chaos, Solitons & Fractals, Vol. 78, (2015), pp. 1–9.
[35] 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 robotâ€, Archives of Control Sciences, Vol. 27, No. 4, (2017), pp. 541–554.
[36] S. Iqbal, X. Zang, Y. Zhu and J. Zhao, “Bifurcations and chaos in passive dynamic walking: A reviewâ€, Robotics and Autonomous Systems, Vol. 62, No. 6, (2014), pp. 889–909.
[37] S.M. Jafarov, E.R. Zeynalov and A.M. Mustafayeva, “Synthesis of the optimal fuzzy T-S controller for the mobile robot using the chaos theoryâ€, Procedia Computer Science, Vol. 102, (2016), pp. 302–308.
[38] 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 navigationâ€, Studies in Computational Intelligence, Vol. 636, (2016), pp. 283–310.
[39] C.K. Volos, V.T. Pham, S. Vaidyanathan, I.M. Kyprianidis and I.N. Stouboulos, “Synchronization phenomena in coupled Colpitts circuitsâ€, Journal of Engineering Science and Technology Review, Vol. 8, No. 2, (2015), pp. 142–151.
[40] C. Jayawickrama, S. Kumar and H. Song, “Novel wideband chaotic approach LNA with microcontroller compatibility for 5G wireless secure communicationâ€, Microwave and Optical Technology Letters, Vol. 60, No. 2, (2018), pp. 48–494.
[41] A. Sambas, W. S. M. Sanjaya, M. Mamat and R. P. Prastio, “Mathematical modelling of chaotic Jerk circuit and its application in secure communication Systemâ€, Studies in Fuzziness and Soft Computing, Vol. 337, (2016), pp. 133-153.
[42] S. Khorashadizadeh and M.H. Majidi, “Chaos synchronization using the Fourier series expansion with application to secure communicationsâ€, AEU-International Journal of Electronics and Communications, Vol. 82, (2017), pp. 37–44.
[43] E.N. Lorenz, “Deterministic nonperiodic flowâ€, Journal of the Atmospheric Sciences, Vol. 20, (1963), pp. 130–141.
[44] J. L¨u and G. Chen, “A new chaotic attractor coinedâ€, International Journal of Bifurcation and Chaos, Vol. 9, (1999), pp. 1465–1466.
[45] G. Tigan and D. Opris, “Analysis of a 3D chaotic systemâ€, Chaos, Solitons and Fractals, Vol. 36, (2008), pp. 1315–1319.
[46] C.H. Lien, S. Vaidyanathan, A. Sambas, Sukono, M. Mamat, W.S.M. Sanjaya and Subiyanto, “A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit designâ€, IOP Conference Series: Materials Science and Engineering, Vol. 332, No. 1, (2018), art. no. 012010.
[47] S. Vaidyanathan, “Global chaos control and synchronization of a novel two-scroll chaotic system with three quadratic nonlinearitiesâ€, Studies in Computational Intelligence, Vol. 636, (2016), pp. 235–255.
[48] S. Vaidyanathan and K. Rajagopal, “Analysis, control, synchronization and LabVIEW implementation of a seven-term novel chaotic systemâ€, International Journal of Control Theory and Applications, Vol. 9, No. 1, (2016), pp. 151–174.
[49] S. Vaidyanathan and A. Boulkroune, “A novel hyperchaotic system with two quadratic nonlinearities, its analysis and synchronization via integral sliding mode controlâ€, International Journal of Control Theory and Applications, Vol. 9, No. 1, (2016), pp. 321–337.
[50] P. Zheng, W. Tang and J. Zhang, “Some novel double-scroll chaotic attractors in Hopfield networksâ€, Neurocomputing, Vol. 73, Nos. 10–12, (2010), pp. 2280–2285.
[51] S. Dadras and H.R. Momeni, “Generating one-, two-, three- and four scroll attractors from a novel four-dimensional smooth autonomous chaotic systemâ€, Chinese Physics B, Vol. 19, (2009), art. no. 060506.
[52] L. Pan, W. Zhou, J. Fang and D. Li, “A new three-scroll unified chaotic system coinedâ€, International Journal of Nonlinear Science, Vol. 10,(2010), pp. 462–474.
[53] S. Vaidyanathan, “Mathematical analysis, adaptive control and synchronization of a ten-term novel three-scroll chaotic system with four quadratic nonlinearitiesâ€, International Journal of Control Theory and Applications, Vol. 9, No. 1, (2016), pp. 1–20.
[54] Z. Wang, Y. Sun, B.J. van Wyk, G. Qi and M.A. van Wyk, “A 3-D four-wing attractor and its analysisâ€, Brazilian Journal of Physics, Vol. 39, (2009), pp. 547–553.
[55] J. Lu, G. Chen and D. Cheng, “A new chaotic system and beyond: the generalized Lorenz-like systemâ€, International Journal of Bifurcation and Chaos, Vol. 14, (2004), pp. 1507–137.
[56] W. Liu and G. Chen, “Can a three-dimensional smooth autonomous quadratic chaotic system generate a single four-scroll attractor?â€, International Journal of Bifurcation and Chaos, Vol. 14, (2004), pp. 1395–1403.
[57] S. Sampath, S. Vaidyanathan, C.K. Volos and V.T. Pham, “An eightterm novel four-scroll chaotic system with cubic nonlinearity and its circuit simulationâ€, Journal of Engineering Science and Technology Review, Vol. 8, (2015), pp. 1–6.
[58] A. Akgul, I. Moroz, I. Pehlivan and S. Vaidyanathan, “A new fourscroll chaotic attractor and its engineering applicationsâ€, Optik, Vol. 127, No. 13, (2016), pp. 5491–5499.
[59] X.S. Yang and Q. Li, “Generate n-scroll attractor in linear system by scalar output feedbackâ€, Chaos, Solitons & Fractals, Vol. 18, (2003), pp. 25–29.
[60] F. Yu, P. Li, K. Gu and B. Yin, “Research progress of multi-scroll chaotic oscillators based on current-mode devicesâ€, Optik, Vol. 13, (2016), pp. 5486–5490.
[61] L. Chen, “A framework to enhance security of physically unclonable functions using chaotic circuitsâ€, Physics Letters A, Vol. 382, No. 18, (2018), pp. 1195–1201.
[62] C. Volos, J.O. Maaita, S. Vaidyanathan, V.T. Pham, I. Stouboulos and I. Kyprianidis, “A novel four-dimensional hyperchaotic four-wing system with a saddle-focus equilibriumâ€, IEEE Transactions on Circuits and Systems-II: Express Briefs, Vol. 64, No. 3, (2017), pp. 339–343.
[63] V.T. Pham, S. Jafari, C. Volos, A. Giakoumis, S. Vaidyanathan and T. Kapitaniak, “A chaotic system with equilibria located on the rounded square loop and its circuit implementationâ€, IEEE Transactions on Circuits and Systems-II: Express Briefs, Vol. 63, No. 9, (2016), pp.878–882.
[64] X. Zhang, Z. Li and D. Chang, “Dynamics, circuit implementation and synchronization of a new three-dimensional fractional-order chaotic systemâ€, AEU - International Journal of Electronics and Communications, Vol. 82, (2017), pp. 435–445.
[65] S. Behnia, Z. Pazhotan, N. Ezzati and A. Akhshani, “Reconfigurable chaotic logic gates based on novel chaotic circuitâ€, Chaos, Solitons & Fractals, Vol. 69, (2014), pp. 74–80.
[66] A. Sambas, Mujiarto, M. Mamat, and W.S.M. Sanjaya, “Numerical simulation and circuit implementation for a sprott chaotic system with one hyperbolic sinusoidal nonlinearityâ€, Far East Journal of Mathematical Sciences, Vol. 102, No. 6, (2017), pp. 1165–1177.
[67] A. Sambas, S. Vaidyanathan, M. Mamat, W.S.M. Sanjaya and R.P.Prastio, “Design, analysis of the Genesio-Tesi chaotic system and its electronic experimental implementationâ€, International Journal of Control Theory and Applications, Vol. 9, No. 1, (2016), pp. 141–149.
[68] S. Vaidyanathan, A.T. Azar, K. Rajagopal, A. Sambas, S. Kacar and U. Cavusoglu, “A new hyperchaotic temperature fluctuations model, its circuit simulation, FPGA implementation and an application to image encryptionâ€, International Journal of Simulation and Process Modelling, Vol. 13, No. 3, (2018), pp. 281–296.
[69] E. Tlelo-Cuautle, J. Rangel-Magdaleno and A.Pano-Azucena, “FPGA realization of multi-scroll chaotic oscillatorsâ€, Communications in Nonlinear Science and Numerical Simulation, Vol. 27, Nos. 1–3, (2015), pp. 66–80.
[70] A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastano, “Determining Lyapunov exponents from a time seriesâ€, Physica D: Nonlinear Phenomena, Vol. 16, No. 3, (1985), pp. 285–317.
-
Downloads
-
How to Cite
Sampath, S., Vaidyanathan, S., Sambas, A., Afendee, M., Mamat, M., & Sanjaya, M. (2018). A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation. International Journal of Engineering & Technology, 7(3), 1931-1935. https://doi.org/10.14419/ijet.v7i3.14865Received date: 2018-06-30
Accepted date: 2018-07-17
Published date: 2018-08-24