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Dynamical properties of a modified chaotic Colpitts oscillator with triangular wave non-linearity

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
Rocznik
Strony
25--53
Opis fizyczny
Bibliogr. 34 poz., rys., tab., wzory
Twórcy
  • Mathematics Section, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences, Ibri, Sultanate of Oman
  • Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India
  • Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India
  • Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India
  • Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India
  • Faculty of Computer Science and Mathematics, University of Kufa, Iraq
Bibliografia
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  • [6] A. Čenys, A. Tamasevicius, A. Baziliauskas, R. Krivickas, and E. Lindberg: Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals, 17(2-3), (2003), 349-353. DOI: 10.1016/S0960-0779(02)00373-9.
  • [7] C.M. Kim, S. Rim, W.H. Kye, J.W. Ryu, and Y.J. Park: Anti-synchronization of chaotic oscillators. Physics Letters A, 320(1), (2003), 39-46. DOI: 10.1016/j.physleta.2003.10.051.
  • [8] A.S. Elwakil and M.P. Kennedy: A family of Colpitts-like chaotic oscillators. Journal of the Franklin Institute, 336(4), (1999), 687-700. DOI: 10.1016/S0016-0032(98)00046-5.
  • [9] S. Vaidyanathan, A. Sambas and S. Zhang: A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model. Archives of Control Sciences, bf 29(3), 2019, 485-506. DOI: 10.24425/acs.2019.130202.
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  • [12] N.J. Corron, S.D. Pethel, and B.A. Hopper: Controlling chaos with simple limiters. Physical Review Letters, 84(17), (2000), 3835. DOI: 10.1103/PhysRevLett.84.3835.
  • [13] J.Y. Effa, B.Z. Essimbi, and J.M. Ngundam: Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control. Nonlinear Dynamics, 58(1-2), (2009), 39. DOI: 10.1007/s11071-008-9459-7.
  • [14] S. Mishra, A.K. Singh and R.D.S. Yadava: Effects of nonlinear capacitance in feedback LC-tank on chaotic Colpitts oscillator. Physica Scripta, 95(5), (2020), 055203. DOI: 10.1088/1402-4896/ab6f95.
  • [15] S. Vaidyanathan and S. Rasappan: Global chaos synchronization of n-scroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arabian Journal for Science and Engineering, 39(4), (2014), 3351-3364. DOI: 10.1007/s13369-013-0929-y.
  • [16] R. Suresh and V. Sundarapandian: Hybrid synchronization of n-scroll Chua and Lure chaotic system using backstepping contol via noval feedback. Archives of Control Science, 22(3), (2012), 255-278. DOI: 10.2478/v10170-011-0028-9.
  • [17] S. Rasappan, R. Murugesan, N.K. Jothi, and S.K. Kumaravel: An observer based chaos synchronization of time delay Takagi-Sugeno fuzzy stochastic system. Far East Journal of Mathematical Sciences, 101(10), (2017), 2195-2217. DOI: 10.17654/MS101102195.
  • [18] R. Suresh: Synchronization of neuronal bursting using backstepping control with recursive feedback. Archives of Control Sciences, 29(4), (2019), 617-642. DOI: 10.24425/acs.2019.131229.
  • [19] H.B. Fotsin and J. Daafouz: Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification. Physics Letters A, 339(3-5), (2005), 304-315. DOI: 10.1016/j.physleta.2005.03.049.
  • [20] S. Sarkar, S. Sarkar, and B.C. Sarkar: On the dynamics of a periodic Colpitts oscillator forced by periodic and chaotic signals. Communications in Nonlinear Science and Numerical Simulation, 19(8), (2014), 2883-2896. DOI: 10.1016/j.cnsns.2014.01.004.
  • [21] R. Suresh and K.A. Niranjan Kumar: Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator. Archives of Control Sciences, 31(3), (2021), 731-759. DOI: 10.24425/acs.2021.138699.
  • [22] S.T. Kammogne and H.B. Fotsin: Synchronization of modified Colpitts oscillators with structural perturbations. Physica Scripta, 83(6), (2011), 065011 DOI: 10.1088/0031-8949/83/06/065011.
  • [23] S.T. Kammogne and H.B. Fotsin: Adaptive control for modified projective synchronization-based approach for estimating all parameters of a class of uncertain systems: Case of modified Colpitts oscillators. Journal of Chaos, (2014). DOI: 10.1155/2014/659647.
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  • [26] S. Bumeliene, A. Tamasevicius, G. Mykolaitis, A. Baziliauskas, and E. Lindberg: Numerical investigation and experimental demonstration of chaos from two-stage Colpitts oscillator in the ultrahigh frequency range. Nonlinear Dynamics, 44(1-4), (2006), 167-172. DOI: 10.1007/s11071-006-1962-0.
  • [27] F.Q. Wu, J. Ma, and G.D. Ren: Synchronization stability between initial-dependent oscillators with periodical and chaotic oscillation. Journal of Zhejiang University-Science A, 19(12), (2018), 889-903. DOI: 10.1631/jzus.A1800334.
  • [28] G.H. Li, S.P. Zhou, and K. Yang: Controlling chaos in Colpitts oscillator. Chaos, Solitons & Fractals, 33(2), (2007), 582-587. DOI: 10.1016/j.chaos.2006.01.072.
  • [29] J.H. Park: Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. Journal of Computational and Applied Mathematics, 213(1), (2008), 288-293. DOI: 10.1016/j.cam.2006.12.003.
  • [30] M. Rehan: Synchronization and anti-synchronization of chaotic oscillators under input saturation. Applied Mathematical Modelling, 37(10-11), (2013), 6829-6837. DOI: 10.1016/j.apm.2013.02.023.
  • [31] M.C. Liao, G. Chen, J.Y. Sze, and C.C. Sung: Adaptive control for promoting synchronization design of chaotic Colpitts oscillators. Journal of the Chinese Institute of Engineers, 31(4), (2008), 703-707. DOI: 10.1080/02533839.2008.9671423.
  • [32] S. Rasappan and S. Vaidyanathan: Hybrid synchronization of n-scroll chaotic Chua circuits using adaptive backstepping control design with recursive feedback. Malaysian Journal of Mathematical Sciences, 7(2), (2013), 219-246.
  • [33] W. Hahn: Stability of Motion. 138 Berlin: Springer, 1967.
  • [34] A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano: Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), (1985), 285-317. DOI: 10.1016/0167-2789(85)90011-9.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cc01e3ca-67c5-4a99-8bf0-8930d8e6db19
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