A New Two-Wing Chaotic System with Line Equilibrium, its Analysis, Adaptive Synchronization and Circuit Simulation

  • Authors

    • Sundarapandian Vaidyanathan Vel Tech University
    • Aceng Sambas Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia
    • Diandra Chika Fransisca Sekolah Tinggi Ilmu Komputer Yos Sudarso Purwokerto
    • Mohamad Afendee Mohamed Universiti Sultan Zainal Abidin
    • Mustafa Mamat Universiti Sultan Zainal Abidin
    2018-11-11
    https://doi.org/10.14419/ijet.v7i4.19507
  • Chaos, chaotic systems, line equilibrium, synchronization, circuit simulation
  • This work reports a new three-dimensional chaotic system with line equilibrium and two equilibrium points on the (x, y) plane. A qualitative analysis has been conducted on the system with the aid of bifurcation diagram, Lyapunov exponents spectrum, etc. It is shown that the new chaotic system is dissipative. Since the new chaotic system has infinitely many equilibrium points, it exhibits hidden attractor. Using adaptive control, global chaos synchronization of the new chaotic system with itself is established using Lyapunov stability theory. Finally, a circuit simulation of the new chaotic system with line equilibrium is carried out via MultiSim and the feasibility of implementing the new chaotic system is established.

  • References

    1. [1] V.T. Pham, S. Vaidyanathan, C. Volos and T. Kapitaniak, Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors, Springer, Berlin, Germany, (2018).

      [2] A.T. Azar and S. Vaidyanathan, Advances in Chaos Theory and Intelligent Control, Springer, Berlin, Germany, (2017).

      [3] 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.

      [4] D. Orrell, “Role of the metric in forecast error growth: how chaotic is the weather?â€, Tellus A: Dynamic Meteorology and Oceanography, Vol. 54, No. 4, (2002), pp. 350–362.

      [5] M.O. Fen, “Persistence of chaos in coupled Lorenz systemsâ€, Chaos, Solitons and Fractals, Vol. 95, (2017), pp. 200–205.

      [6] 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.

      [7] T. Akaishi, T. Takahashi and I. Nakashima, “Chaos theory for clinical manifestations in multiple sclerosisâ€, Medical Hypotheses, Vol. 115, (2018), pp. 87–93.

      [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] S. Vaidyanathan, “Adaptive control of the FitzHugh-Nagumo chaotic neuron modelâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 117–127.

      [10] S. Vaidyanathan, “Analysis, control, and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearitiesâ€, Kyungpook Mathematical Journal, Vol. 55, No. 3, (2015), pp. 563–586.

      [11] C. Li, J.C. Sprott and H. Xing, “Hypogenetic chaotic jerk flowsâ€, Physics Letters A, Vol. 380, (2016), pp. 1172–1177.

      [12] X. Wang, S. Vaidyanathan, C. Volos, V.T. Pham and T. Kapitaniak, “Dynamics, circuit realization, control and synchronization of a hyperchaotic hyperjerk system with coexisting attractorsâ€, Nonlinear Dynamics, Vol. 89, No. 3, (2017), pp. 1673–1687.

      [13] S. Vaidyanathan, S.T. Kingni, A. Sambas, M.A. Mohamed and M. Mamat, “A new chaotic jerk system with three nonlinearities and synchronization via adaptive backstepping controlâ€, International Journal of Engineering and Technology, Vol. 7, No. 3, (2018), pp. 1936–1943.

      [14] J. Chattopadhyay, N. Pal, S. Samanta, E. Venturino and Q.J.A. Khan, “Chaos control via feeding switching in an omnivory systemâ€, Biosystems, Vol. 138, (2015), pp. 18–24.

      [15] V. Voorsluijs and Y.D. Decker, “Emergence of chaos in a spatially confined reactive systemâ€, Physica D: Nonlinear Phenomena, Vol. 335, (2016), pp. 1–9.

      [16] 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.

      [17] O.I. Tacha, C.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.

      [18] B.A. Idowu, S. Vaidyanathan, A. Sambas, O.I. Olusola and O.S. Onma, “A new chaotic finance system: Its analysis, control, synchronization and circuit designâ€, Studies in Systems, Decision and Control, Vol. 133, (2018), pp. 271–295.

      [19] X. J. Tong, M. Zhang, Z.Wang, Y. Liu and J. Ma, “An image encryption scheme based on a new hyperchaotic finance systemâ€, Optik, Vol. 126, No. 20, (2015), pp. 2445–2452.

      [20] I. Klioutchnikov, M. Sigova and N. Beizerova, “Chaos theory in financeâ€, Procedia Computer Science, Vol. 119, (2017), pp. 368–375.

      [21] S. Vaidyanathan, “Adaptive controller and synchronization design for the Qi-Chen chaotic systemâ€, Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, Vol. 85, (2012), pp. 124–133.

      [22] 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.

      [23] 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.

      [24] S. Vaidyanathan, “Chaos in neurons and synchronization of Birkhoff-Shaw strange chaotic attractors via adaptive controlâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 1–11.

      [25] S. Vaidyanathan, “Hyperchaos, qualitative analysis, control and synchronization of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearitiesâ€, International Journal of Modelling, Identification and Control, Vol. 23, No. 4, (2015), pp. 380–392.

      [26] J. Jin, “Programmable multi-direction fully integrated chaotic oscillatorâ€, Microelectronics Journal, Vol. 75, (2018), pp. 27–34.

      [27] S. Vaidyanathan, “Analysis and synchronization of the hyperchaotic Yujun systems via sliding mode controlâ€, Advances in Intelligent Systems and Computing, Vol. 176, (2012), pp. 329–337.

      [28] S. Pakiriswamy and S. Vaidyanathan, “Generalized projective synchronization of three-scroll chaotic systems via active controlâ€, Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, Vol. 85, (2012), pp. 146–155.

      [29] M.H. Wang, S.D. Lu and M.J. Hsieh, “Application of extension neural network algorithm and chaos synchronization detection method to partial discharge diagnosis of power capacitorâ€, Measurement, Vol. 129, (2018), pp. 227–235.

      [30] K. Bouallegue, “A new class of neural networks and its applicationsâ€, Neurocomputing, Vol. 249, (2017), pp. 28–47.

      [31] S. Vaidyanathan, “Synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control method â€, International Journal of PharmTech Research, Vol. 8, No. 5, (2015), pp. 946–955.

      [32] S. Vaidyanathan, “A novel chemical chaotic reactor system and its adaptive controlâ€, International Journal of ChemTech Research, Vol. 8, No. 7, (2015), pp. 146–158.

      [33] V.K. Yadav, B.S. Bhadauria, A.K. Singh and M. Srivastava, “Stability analysis, chaos control of a fractional order chaotic chemical reactor system and its function projective synchronization with parametric uncertaintiesâ€, Chinese Journal of Physics, Vol. 55, No. 3, (2017), pp. 594–605.

      [34] 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.

      [35] S. Vaidyanathan, “Global chaos synchronization of chemical chaotic reactors via novel sliding mode control methodâ€, International Journal of ChemTech Research, Vol. 8, No. 7, (2015), pp. 209–221.

      [36] S. Vaidyanathan, A. Akgul, S. Kacar and U. Cavusoglu, “A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganographyâ€, European Physical Journal Plus, Vol. 133, (2018), Article ID 46.

      [37] N. Kar, K. Mandal and B. Bhattacharya, “Improved chaos-based video steganography using DNA alphabetsâ€, ICT Express, Vol. 133, (2018), pp. 6–13.

      [38] Y.R. Bai, D. Baleanu and G.C. Wu, “A novel shuffling technique based on fractional chaotic mapsâ€, Optik, Vol. 168, (2018), pp. 553-562.

      [39] G.C.Wu, D. Baleanu and Z.X. Lin, “Image encryption technique based on fractional chaotic time seriesâ€, Journal of Vibration and Control, Vol. 22, No. 8 (2014), pp. 2092–2099.

      [40] S. Vaidyanathan, A. Sambas, M. Mamat and M. Sanjaya WS, “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.

      [41] C. Cao, K. Sun and W. Liu, “ A novel bit-level image encryption algorithm based on 2D-LICM hyperchaotic mapâ€, Signal Processing, Vol. 143,(2018), pp. 122–133.

      [42] B.K. Patle, D.R.K. Parhi, A. Jagadeesh and S.K. Kashyap, “Matrix-Binary Codes based Genetic Algorithm for path planning of mobile robotâ€, Computers & Electrical Engineering, Vol. 67, (2018), pp. 708–728.

      [43] S. Vaidyanathan, A. Sambas, M. Mamat and M. Sanjaya WS, “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.

      [44] A. Sambas, S. Vaidyanathan, M. Mamat and W.S. Mada Sanjaya, “A six-term novel chaotic system with hidden attractor and its circuit designâ€, Studies in Systems, Decision and Control, Vol. 133, (2018), pp. 365–373.

      [45] S. Sampath, S. Vaidyanathan, A. Sambas, M.A. Mohamed, M. Mamat and W.S. Mada Sanjaya, “A new four-scroll chaotic system with a selfexcited attractor and circuit implementationâ€, International Journal of Engineering and Technology, Vol. 7, No. 3, (2018), pp. 1931–1935.

      [46] K. Sun, X. Liu and C. Zhu, “Dynamics of a strengthened chaotic system and its circuit implementationâ€, Chinese Journal of Electronics, Vol. 23, No. 2, (2014), pp. 353–356.

      [47] J. Mou, K. Sun, J. Ruan and S. He, “A nonlinear circuit with two memcapacitorsâ€, Nonlinear Dynamics, Vol. 86, No. 23, (2016), pp. 1735–1744.

      [48] M. Mamat, S. Vaidyanathan, A. Sambas, Mujiarto,W.S.M. Sanjaya and Subiyanto, “A novel double-convection chaotic attractor, its adaptive control and circuit simulationâ€, IOP Conference Series: Materials Science and Engineering, Vol. 332, No. 1, (2018), Article ID 012033.

      [49] S. Vaidyanathan, A. Sambas, Sukono, M. Mamat, G. Gundara, W.S. Mada Sanjaya and Subiyanto, “A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementationâ€, IOP Conference Series: Materials Science and Engineering, Vol. 332, No. 1, (2018), Article ID 012048.

      [50] 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), Article ID 012010.

      [51] A. Sambas, M. Mamat, S. Viadyanathan, M. A. Mohamed and W. S. Mada Sanjaya, “A new 4-D chaotic system with hidden attractor and its circuit implementationâ€, International Journal of Engineering & Technology, Vol. 7, No. 3, (2018), pp. 1245–1250.

      [52] M. Mamat, S. Vaidyanathan, A. Sambas, M.A. Mohamed, S. Sampath and W.S. Mada Sanjaya, “A new 3-D chaotic system with conch shaped equilibrium curve and its circuit implementationâ€, International Journal of Engineering & Technology, Vol. 7, No. 3, (2018), pp. 1410–1414.

      [53] S. Vaidyanathan, A. Sambas, M.A. Mohamed, M. Mamat and W.S. Mada Sanjaya, “A new hyperchaotic hyperjerk system with three nonlinear terms, its synchronization and circuit simulationâ€, International Journal of Engineering & Technology, Vol. 7, No. 3, (2018), pp. 1585–1592.

      [54] A. Sambas, M. Mamat, S. Vaidyanathan, M.A. Mohamed, W.S. Mada Sanjaya and Mujiarto, “A novel chaotic hidden attractor, its synchronization and circuit implementationâ€, WSEAS Transactions on Systems and Control, Vol. 13, (2018), pp. 345–352.

      [55] V.T. Pham, S. Vaidyanathan, C.K. Volos, S. Jafari, N.V. Kuznetsov and T.M. Hoang, “A novel memristive time-delay chaotic system without equilibrium pointsâ€, European Physical Journal: Special Topics, Vol. 225, (2016), pp. 127–136.

      [56] S. Jafari and J.C. Sprott, “Simple chaotic flows with a line equilibriumâ€, Chaos, Solitons and Fractals, Vol. 57, (2013), pp. 79–84.

      [57] C. Li, J.C. Sprott and W. Thioc, “Bistability in a hyperchaotic system with a line equilibriumâ€, Experimental and Theoretical Physics, Vol. 118, No. 3, (2014), pp. 494–500.

      [58] C. Li, J.C. Sprott, Z. Yuan and H. Li “Constructing chaotic systems with total amplitude controlâ€, International Journal of Bifurcation and Chaos, Vol. 25, No. 10, (2015), pp. 1530025.

      [59] F. Nazarimehr, K. Rajagopal, J. Kengne, S. Jafari and V.T. Pham, “A new four-dimensional system containing chaotic or hyper-chaotic attractors with no equilibrium, a line of equilibria and unstable equilibriaâ€, Chaos, Solitons and Fractals, Vol. 111, (2018), pp. 108–118.

      [60] V.T. Pham, S. Jafari and C. Volos, “A novel chaotic system with heartshaped equilibrium and its circuital implementationâ€, Optik, Vol. 131, (2017), pp. 343–349.

      [61] T. Gotthans and J. Petrzela, “New class of chaotic systems with circular equilibriumâ€, Nonlinear Dynamics, Vol. 81, No. 3, (2015), pp. 1143–1149.

      [62] T. Gotthans, J.C. Sprott and J. Petrzela, “Simple chaotic flow with circle and square equilibriumâ€, International Journal of Bifurcation and Chaos, Vol. 26, No. 8, (2016), pp. 1650137.

      [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] S.T. Kingni, V.T. Pham, S. Jafari and P. Woafo, “A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order formâ€, Chaos, Solitons and Fractals, Vol. 99, No. 1, (2017), pp. 209–218.

      [65] S. Vaidyanathan, A. Sambas, S. Kacar and U. Cavusoglu, “A new threedimensional chaotic system with a cloud-shaped curve of equilibrium points, its circuit implementation and sound encryptionâ€, International Journal of Modelling, Identification and Control, Vol. 30, No. 3, (2018), pp. 184–196.

      [66] E.N. Lorenz, “Deterministic nonperiodic flowâ€, Journal of the Atmospheric Sciences, Vol. 20, (1963), pp. 130–140.

      [67] G. Chen and T. Ueta, “Yet another chaotic attractorâ€, International Journal of Bifurcation and Chaos, Vol. 9, (1999), pp. 1465–1466.

      [68] J. Lu and G. Chen, “A new chaotic attractor coinedâ€, International Journal of Bifurcation and Chaos, Vol. 12, (1963), pp. 130–140.

      [69] C. Liu, T. Liu, L. Liu and K. Liu, “A new chaotic attractorâ€, Chaos, Solitons and Fractals, Vol. 22, (2004), pp. 1031–1038.

      [70] G. Tigan and D. Opris, “Analysis of a 3D chaotic systemâ€, Chaos, Solitons and Fractals, Vol. 36, (2008), pp. 1315–1319.

      [71] S. He, K. Sun and S. Banerjee, “ Dynamical properties and complexity in fractional-order diffusionless Lorenz systemâ€, The European hysical Journal Plus, Vol. 131, No. 8, (2016), pp. 254.

      [72] C. Li, L. Wu, H. Li and Y. Tong, “A novel chaotic system and its topological horseshoeâ€, Nonlinear Analysis: Modelling and Control, Vol. 18, (2013), pp. 66–77.

      [73] S. Rasappan and S. Vaidyanathan, “Synchronization of hyperchaotic Liu system via backstepping control with recursive feedbackâ€, Communications in Computer and Information Science, Vol. 305, (2012), pp. 212–221.

      [74] Y. Wang, K. Sun, S. He and H. Wang “Dynamics of fractional-order sinusoidally forced simplified Lorenz system and its synchronizationâ€, The European Physical Journal Special Topics, Vol. 223, No. 8, (2014), pp. 1591–1600.

      [75] S. Vaidyanathan, “Global chaos synchronization of the Lotka-Volterra biological systems with four competitive species via active controlâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 206–217.

      [76] S. Vaidyanathan and S. Pakiriswamy, “The design of active feedback controllers for the generalized projective synchronization of hyperchaotic Qi and hyperchaotic Lorenz systemsâ€, Communications in Computer and Information Science, Vol. 245, (2011), pp. 231–238.

      [77] S. Vaidyanathan and S. Pakiriswamy, “Generalized projective synchronization of double-scroll chaotic systems using active feedback controlâ€, Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, Vol. 84, (2012), pp. 111–118.

      [78] S. Vaidyanathan, “Global chaos synchronization of the Lotka-Volterra biological systems with four competitive species via active controlâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 206–217.

      [79] U.E. Kocamaz, Y. Uyaroglu and H. Kizmaz, “Controlling hyperchaotic Rabinovich system with single state controllers: Comparison of linear feedback, sliding mode, and passive control methodsâ€, Optik, Vol. 130, (2017), pp. 914–921.

      [80] X. Chen and C. Liu, “Passive control on a unified chaotic systemâ€, Nonlinear Analysis: Real World Applications, Vol. 11, No. 2, (2010), pp. 683–687.

      [81] S. Vaidyanathan, “ A novel four-ensional conservative chaotic system without linear term, its analysis and adaptive control via integral sliding mode controlâ€, International Journal of Modelling, Identification and Control, Vol. 30, No. 2, (2018), pp. 132–142.

      [82] S. Vaidyanathan, “Super-twisting sliding mode control and synchronization of Moore-Spiegel thermo-mechanical chaotic systemâ€, Studies in Computational Intelligence, Vol. 709, (2017), pp. 451–470.

      [83] S. Vaidyanathan and S. Sampath, “Sliding mode controller design for the global chaos synchronization of Coullet systemsâ€, Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, Vol. 84, (2012), pp. 103–110.

      [84] S. Vaidyanathan, “Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system via backstepping control methodâ€, Archives of Control Sciences, Vol. 26, No. 3, (2016), pp. 311–338.

      [85] S. Rasappan and S. Vaidyanathan, “Synchronization of hyperchaotic Liu system via backstepping control with recursive feedbackâ€, Communications in Computer and Information Science, Vol. 305, (2012), pp. 212–221.

      [86] S. Vaidyanathan and A.T. Azar, “A novel 2-D chaotic enzymessubstrates reaction system and its adaptive backstepping controlâ€, Studies in Fuzziness and Soft Computing, Vol. 337, (2016), pp. 507–528.

      [87] S. Vaidyanathan, “Adaptive synchronization of the identical FitzHugh-Nagumo chaotic neuron modelsâ€, International Journal of PharmTech Research, Vol. 8, No. 6, (2015), pp. 167–177.

      [88] X. Zhang, D. Li and X. Zhang, “Adaptive fuzzy impulsive synchronization of chaotic systems with random parametersâ€, Chaos, Solitons and Fractals, Vol. 104, (2017), pp. 77–83.

      [89] S. Vaidyanathan, “Qualitative analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with a quartic nonlinearityâ€, International Journal of Control Theory and Applications, Vol. 7, No. 1, (2014), pp. 1–10.

      [90] A. Akgul, I. Moroz, I. Pehlivan and S. Vaidyanathan, “A new four-scroll chaotic attractor and its engineering applicationsâ€, Optik, Vol. 127, No. 13, (2016), pp. 5491–5499.

      [91] S. Vaidyanathan, M. Feki, A. Sambas and C.H. Lien, “A new biological snap oscillator: its modelling, analysis, simulations and circuit designâ€, International Journal of Simulation and Process Modelling, Vol. 13, No. 5, (2018), pp. 419–432.

      [92] S. Sampath, S. Vaidyanathan, A. Sambas, M.A. Mohamed, M. Mamat and W.S. Mada Sanjaya, “A new four-scroll chaotic system with a selfexcited attractor and circuit implementationâ€, International Journal of Engineering & Technology, Vol. 7, No. 3, (2018), pp. 1931–1935.

      [93] S. Vaidyanathan, S.T. Kingni, A. Sambas, M. A. Mohamed and M. Mamat, “A new chaotic jerk system with three nonlinearities and synchronization via adaptive backstepping controlâ€, International Journal of Engineering & Technology, Vol. 7, No. 3, (2018), pp. 1936–1943.

      [94] H.T. Khalil, Nonlinear Systems, Pearson, Indiana, USA, (2001).

      [95] 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.

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    Vaidyanathan, S., Sambas, A., Fransisca, D. C., Mohamed, M. A., & Mamat, M. (2018). A New Two-Wing Chaotic System with Line Equilibrium, its Analysis, Adaptive Synchronization and Circuit Simulation. International Journal of Engineering & Technology, 7(4), 3739-3746. https://doi.org/10.14419/ijet.v7i4.19507