Details

Title

Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator

Journal title

Archives of Control Sciences

Affiliation

Rasappan, Suresh : Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India ; Niranjan Kumar, K.A. : Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India

Authors

Keywords

chaos ; Colpitts oscillator ; Lyapunov exponent ; diffusion ; stability ; synchronization

Divisions of PAS

Nauki Techniczne

Coverage

731-759

Publisher

Committee of Automatic Control and Robotics PAS

Bibliography

[1] M.P. Kennedy: Chaos in the Colpitts oscillator. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 41 (1994), 771–774, DOI: 10.1109/81.331536.
[2] S. Vaidyanathan, K. Rajagopal, C.K. Volos, I.M. Kyprianidis, and I.N. Stouboulos: Analysis, adaptive control and synchronization of a seventerm novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in labview. Journal of Engineering Science and Technology Review, 8 (2015), 130–141.
[3] P. Kvarda: Identifying the deterministic chaos by using the Lyapunov exponents. Radioengineering-Prague, 10 (2001), 38–38.
[4] Y.C. Lai and C. Grebogi: Modeling of coupled chaotic oscillators. Physical Review Letters, 82 (1999), 4803, DOI: 10.1103/PhysRevLett.82.4803.
[5] H. Deng and D. Wang: Circuit simulation and physical implementation for a memristor-based Colpitts oscillator. AIP Advances, 7 (2017), 035118, DOI: 10.1063/1.4979175.
[6] A. Cenys, A. Tamasevicius, A.Baziliauskas, R. Krivickas, and E. Lind- berg: Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals, 17 (2003), 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 (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 (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, 29 (2019), DOI: 10.24425/acs.2019.130202.
[10] C.K. Volos, V.T. Pham, S. Vaidyanathan, I.M. Kyprianidis, and I.N. Stouboulos: Synchronization phenomena in coupled Colpitts circuits. Journal of Engineering Science & Technology Review, 8 (2015).
[11] H. Fujisaka and T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems. Progress of theoretical physics, 69 (1983), 32– 47, DOI: 10.1143/PTP.69.32.
[12] N.J. Corron, S.D. Pethel, and B.A. Hopper: Controlling chaos with simple limiters. Physical Review Letters, 84 (2000), 3835, DOI: 10.1103/Phys-RevLett.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 (2009), 39–47, 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 (2020), 055203. DOI: 10.1088/1402-4896/ab6f95.
[15] S. Vaidyanathan and S. Rasappan: Global chaos synchronization of nscroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arabian Journal for Science and Engineering, 39 (2014), 3351–3364, DOI: 10.1007/s13369-013-0929-y.
[16] R. Suresh and V. Sundarapandian: Hybrid synchronization of nscroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Archives of Control Sciences, 22 (2012), 343–365, DOI: 10.2478/v10170-011-0028-9.
[17] S. Rasappan: Synchronization of neuronal bursting using backstepping control with recursive feedback. Archives of Control Sciences, 29 (2019), 617–642, DOI: 10.24425/acs.2019.131229.
[18] H.B. Fotsin and J.Daafouz:Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification. Physics Letters A, 339 (2005), 304–315, DOI: 10.1016/j.physleta.2005.03.049.
[19] 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 (2014), 2883–2896, DOI: 10.1016/j.cnsns.2014.01.004.
[20] S.T. Kammogne and H.B. Fotsin: Synchronization of modified Colpitts oscillators with structural perturbations. Physica scripta, 83 (2011), 065011, DOI: 10.1088/0031-8949/83/06/065011.
[21] 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.
[22] L.M. Pecora and T.L. Carroll: Synchronization in chaotic systems. Physical review letters, 64 (1990), 821, DOI: 10.1103/PhysRevLett.64.821.
[23] I. Ahmad and B. Srisuchinwong: A simple two-transistor 4D chaotic oscillator and its synchronization via active control. IEEE 26th International Symposium on Industrial Electronics, (2017) 1249–1254, DOI: 10.1109/ISIE.2017.8001424.
[24] S. Bumelien˙e, A. Tamasevicius, G. Mykolaitis, A. Baziliauskas, and E. Lindber: Numerical investigation and experimental demonstration of chaos from two-stage Colpitts oscillator in the ultrahigh frequency range. Nonlinear Dynamics, 44 (2006), 167–172, DOI: 10.1007/s11071-006-1962-0.
[25] F.Q. Wu, J. Ma, and G.D. Ren: Synchronization stability between initialdependent oscillators with periodical and chaotic oscillation. Journal of Zhejiang University-Science A, 19 (2018), 889–903, DOI: 10.1631/jzus.a1800334.
[26] G.H. Li, S.P. Zhou, and K. Yang: Controlling chaos in Colpitts oscillator. Chaos, Solitons & Fractals, 33 (2007), 582–587, DOI: 10.1016/j.chaos.2006.01.072.
[27] S. Vaidyanathan, S.A.J.A.D. Jafari, V.T. Pham, A.T. Azar, and F.E. Al- saadi: A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design. Archives of Control Sciences, 28 (2018), 239–254, DOI: 10.24425/123458.
[28] 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 (2008), 288–293. DOI: 10.1016/j.cam.2006.12.003.
[29] M. Rehan: Synchronization and anti-synchronization of chaotic oscillators under input saturation. Applied Mathematical Modelling, 37 (2013), 6829– 6837. DOI: 10.1016/j.apm.2013.02.023.
[30] 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 (2008), 703–707. DOI: 10.1080/02533839.2008.9671423.
[31] 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 (2013), 219–246. DOI: 10.1080/23311916.2015.1009273.
[32] J. Kengne, J.C. Chedjou, G. Kenne, and K. Kyamakya: Dynamical properties and chaos synchronization of improved Colpitts oscillators. Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 2914–2923. DOI: 10.1016/j.cnsns.2011.10.038.
[33] W. Hahn: Stability of motion. Springer, 138, 1967.
[34] J.P. Singh and B.K. Roy: The nature of Lyapunov exponents is (+,+,-,-). Is it a hyperchaotic system? Chaos, Solitons & Fractals, 92 (2016), 73–85. DOI: 10.1016/j.chaos.2016.09.010.
[35] A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano: Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16 (1985), 285–317. DOI: 10.1016/0167-2789(85)90011-9.

Date

2021.09.27

Type

Article

Identifier

DOI: 10.24425/acs.2021.138699
×