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Research Article

Controlling the initial condition of coupled synchronization of chaotic fractional Newton-Leipnik system for its stability with minimal order

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Pages 931-945 | Received 01 Jan 2019, Published online: 13 Jan 2021

References

  • M. Khan, “Adaptive synchronization of two coupled Newton-Leipnik systems with uncertain parameter,” Int. J. Basic Appl. Sci., vol. 1, no. 4, pp. 439–447, 2012.
  • M. Hu, “Adaptive feedback controller for projective synchronization,” Nonlinear Anal. Real World Appl., vol. 9, no. 3, pp. 1253–1260, 2008.
  • X. Wang and C. Ge, “Controlling and Tracking of Newton – Leipnik System via Backstepping Design Controlling Newton – Leipnik system,” Int. J. Nonlinear Sci., vol. 5, no. 2, pp. 133–139, 2008.
  • S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Rep., vol. 366, no. 1–2, pp. 1–101, 2002.
  • H. Chen, “Global chaos synchronization of new chaotic systems via nonlinear control,” Chaos, Solitons & Fractals, vol. 23, no. 4, pp. 1245– 1251, 2005.
  • L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett., vol. 64, no. 8, pp. 821–824, Feb. 1990.
  • E. E. Mahmoud, “Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear systems,” Math. Methods Appl. Sci., vol. 37, no. 3, pp. 321–328, 2014.
  • M. Arch, M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett., vol. 1, no. 3, pp. 2–5, 1996.
  • E. S. K. Mbe, H. B. Fotsin, J. Kengne, and P. Woafo, “Parameters estimation based adaptive Generalized Projective Synchronization (GPS) of chaotic Chua’s circuit with application to chaos communication by parametric modulation,” Chaos, Solitons & Fractals, vol. 61, pp. 27–37, 2014.
  • E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, “Lag synchronization in time-delayed systems,” Phys. Lett. A, vol. 292, no. 6, pp. 320–324, Jan. 2002.
  • G. Kaddoum, F.-D. Richardson, and F. Gagnon, “Design and Analysis of a Multi-Carrier Differential Chaos Shift Keying Communication System,” CoRR, vol. abs/1303.3, 2013.
  • K. M. Cuomo and A. V Oppenheim, “Circuit implementation of synchronized chaos with applications to communications,” Phys. Rev. Lett., vol. 71, no. 1, pp. 65–68, Jul. 1993.
  • E.-W. Bai and K. E. Lonngren, “Synchronization of two Lorenz systems using active control,” Chaos, Solitons & Fractals, vol. 8, no. 1, pp. 51–58, Jan. 1997.
  • R. Karthikeyan and V. Sundarapandian, “Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control,” J. Electr. Eng., vol. 65, no. 2, pp. 97–103, 2014.
  • S. Bhalekar and V. Daftardar-Gejji, “Synchronization of different fractional order chaotic systems using active control,” Commun. Nonlinear Sci. Numer. Simul., vol. 15, no. 11, pp. 3536–3546, 2010.
  • A. V Oppenheim, G. W. Wornell, S. H. Isabelle, and K. M. Cuomo, “Signal processing in the context of chaotic signals,” Int. Conf. Acoust. Speech, Signal Process. 1992, vol. 4, pp. 117–120, 1992.
  • S. H. Strogatz and A. V. Oppenheim, “Synchronization of Lorenz-Based Chaotic Circuits with Applications to Communications,” IEEE Trans. Circuits Syst. II Analog Digit. Signal Process., vol. 40, no. 10, pp. 626–633, 1993.
  • W. Li, Z. Yang, and Q. Ding, “Synchronous Digital Signal Communication System Based on Chaotic Masking,” J. Inf. Hiding Multimed. Signal Process., vol. 7, no. 2, pp. 304–316, 2016.
  • R. B. Leipnik and T. A. Newton, “Double strange attractors in rigid body motion with linear feedback control,” Phys. Lett. A, vol. 86, pp. 63–67, Nov. 1981.
  • Y. Kang, K.-T. Lin, J.-H. Chen, L.-J. Sheu, and H.-K. Chen, “Parametric analysis of a fractional-order Newton-Leipnik system,” J. Phys. Conf. Ser., vol. 96, p. 012140, Feb. 2008.
  • M. S. Tavazoei and M. Haeri, “Chaotic attractors in incommensurate fractional order systems,” Phys. D Nonlinear Phenom., vol. 237, no. 20, pp. 2628–2637, Oct. 2008.
  • M. S. Tavazoei and M. Haeri, “Unreliability of frequency-domain approximation in recognising chaos in fractional-order systems,” IET Signal Process., vol. 1, no. 4, pp. 171–181, Dec. 2007.
  • M. S. Tavazoei and M. Haeri, “A necessary condition for double scroll attractor existence in fractional-order systems,” Phys. Lett. A, vol. 367, no. 1–2, pp. 102–113, Jul. 2007.
  • M. S. Tavazoei and M. Haeri, “Limitations of frequency domain approximation for detecting chaos in fractional order systems,” Nonlinear Anal. Theory, Methods Appl., vol. 69, no. 4, pp. 1299–1320, Aug. 2008.
  • L. J. Sheu, H. K. Chen, J. H. Chen, L. M. Tam, W. C. Chen, K. T. Lin, and Y. Kang, “Chaos in the Newton-Leipnik system with fractional order,” Chaos, Solitons and Fractals, vol. 36, no. 1, pp. 98–103, 2008.
  • A. V Oppenheim, G. W. Wornell, S. H. Isabelle, and K. M. Cuomo, “Signal processing in the context of chaotic signals,” in [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992, vol. 4, pp. 117–120 vol.4.
  • “Experimetal Demonstration of secure Communications Via Chaotic Synchronization,” Int. J. Bifurc. Chaos, vol. 02, no. 03, pp. 709–713, 1992.

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