Добавил:
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз: Предмет: Файл:
3703.pdf
Скачиваний:
9
Добавлен:
15.11.2022
Размер:
11.37 Mб
Скачать

Dynamics of Fractional Order Chaotic Systems

33

Figure 4a. Synchronized signals y(t) and y1(t) for α = 0.98.

Figure 4b. Errors in synchronization for α = 0.98.

Acknowledgments

Author acknowledges Shivaji University, Kolhapur for the minor research project grant provided under the “Innovative Research Activities”.

Complimentary Contributor Copy

34

Sachin Bhalekar

References

[1]K.T. Alligood, T.D. Sauer, J. A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer, New York, 2008.

[2]Podlubny, I., Fractional Differential Equations, Academic Press, San Diego (1999).

[3]Samko, S. G., A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon (1993).

[4]Kilbas, A. A., H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).

[5]I. Grigorenko and E. Grigorenko, Chaotic dynamics of the fractional Lorenz system, Phys. Rev. Lett. 91 (2003) 034101.

[6]C. Li, G. Peng, Chaos in Chen's system with a fractional order, Chaos Solitons Fractals 22 (2004) 443–450.

[7]J. G. Lu,¨ Chaotic dynamics of the fractional order Lu¨ system and its synchronization, Phys. Lett. A 354(4) (2006) 305–311.

[8]Li, C. G. and G. Chen, Chaos and hyperchaos in the fractional order Rossler equations,

Phys. A: Stat. Mech. Appl., 341, (2004) 55–61.

[9]Daftardar-Gejji, V. and S. Bhalekar, Chaos in fractional ordered Liu system, Comput. Math. Appl., 59, (2010) 1117–1127.

[10]M. S. Tavazoei and M. Haeri, Regular oscillations or chaos in a fractional order system with any effective dimension, Nonlinear Dynamics, 54(3) (2008) 213–222.

[11]D. Matignon, Stability results for fractional differential equations with applications to control processing. In: Computational Engineering in Systems and Application multiconference, vol. 2, pp. 963-968, IMACS, IEEE-SMC Proceedings, Lille, France, July (1996).

[12]M. S. Tavazoei and M. Haeri, Chaotic attractors in incommensurate fractional order systems, Physica D, 237 (2008) 2628-2637.

[13]W. Deng, C. Li and J. Lu, Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dynamics, 48 (2007) 409-416.

[14]K. Diethelm, N. J. Ford and A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics 29 (2002) 3–22.

[15]K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Elec. Trans. Numer. Anal. 5 (1997) 1–6.

[16]K. Diethelm and N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl. 265 (2002) 229-48.

Complimentary Contributor Copy

Dynamics of Fractional Order Chaotic Systems

35

[17]C. Li, L. Wu, H. Li, Y. Tong, A novel chaotic system and its topological horseshoe,

Nonlinear Analysis: Modelling and Control, 18(1) (2013) 66–77.

[18]E. Ahmed, A.M.A. El-Sayed, H. A.A. El-Saka, On some RouthHurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems, Physics Letters A 358 (2006) 1–4.

[19]E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963) 130.

[20]S. Celikovsky, G. Chen, On the generalized Lorenz canonical form, Chaos Solitons Fractals, 26 (2005), 1271

[21]L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64(8) (1990) 821.

[22]L. M. Pecora and T. L. Carroll, Driving systems with chaotic signals, Phys. Rev. A 44 (1991) 2374.

[23]R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, USA, 2001.

[24]R. He and P. G. Vaidya, Implementation of chaotic cryptography with chaotic synchronization, Phys. Rev. E 57(2) (1998) 1532.

[25]W. H. Deng and C. P. Li, Chaos synchronization of the fractional Lu¨ system, Physica A 353 (2005) 61–72.

Complimentary Contributor Copy

Complimentary Contributor Copy

Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]