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2017 | OriginalPaper | Buchkapitel

Comparison of Three Different Synchronization Schemes for Fractional Chaotic Systems

verfasst von : S. T. Ogunjo, K. S. Ojo, I. A. Fuwape

Erschienen in: Fractional Order Control and Synchronization of Chaotic Systems

Verlag: Springer International Publishing

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Abstract

The importance of synchronization schemes in natural and physical systems including communication modes has made chaotic synchronization an important tool for scientist. Synchronization of chaotic systems are usually conducted without considering the efficiency and robustness of the scheme used. In this work, performance evaluation of three different synchronization schemes: Direct Method, Open Plus Closed Loop (OPCL) and Active control is investigated. The active control technique was found to have the best stability and error convergence. Numerical simulations have been conducted to assert the effectiveness of the proposed analytical results.

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Literatur
1.
Zurück zum Zitat Ahmad, I., Saaban, A. B., & Shahzad, M. (2015). A research on active control to synchronize a new 3D chaotic system. Systems, 4(2), 1–14. doi:10.3390/systems4010002. Ahmad, I., Saaban, A. B., & Shahzad, M. (2015). A research on active control to synchronize a new 3D chaotic system. Systems, 4(2), 1–14. doi:10.​3390/​systems4010002.
2.
Zurück zum Zitat Al-Sawalha, M. M., & Shoaib, M. (2016). Reduced-order synchronization of fractional order chaotic systems with fully unknown parameters using modified adaptive control. Journal of Nonlinear Science and Applications, 9, 1815–1825.MathSciNetMATH Al-Sawalha, M. M., & Shoaib, M. (2016). Reduced-order synchronization of fractional order chaotic systems with fully unknown parameters using modified adaptive control. Journal of Nonlinear Science and Applications, 9, 1815–1825.MathSciNetMATH
4.
Zurück zum Zitat Bai, E. W., & Lonngren, K. E. (1997). Synchronization of two lorenz systems using active control. Chaos, Solitons & Fractals, 8(1), 51–58.CrossRefMATH Bai, E. W., & Lonngren, K. E. (1997). Synchronization of two lorenz systems using active control. Chaos, Solitons & Fractals, 8(1), 51–58.CrossRefMATH
5.
Zurück zum Zitat Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002). The synchronization of chaotic systems. Physics Reports, 366, 1–101.MathSciNetCrossRefMATH Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002). The synchronization of chaotic systems. Physics Reports, 366, 1–101.MathSciNetCrossRefMATH
7.
Zurück zum Zitat Caponetto, R., Dongola, G., Fortuna, L., & Petras, I. (2010). Fractional order systems: Modeling and control applications, A (Vol. 72). World Scientific Publishing Cp. Pte. Ltd. Caponetto, R., Dongola, G., Fortuna, L., & Petras, I. (2010). Fractional order systems: Modeling and control applications, A (Vol. 72). World Scientific Publishing Cp. Pte. Ltd.
8.
Zurück zum Zitat Concepcion, A. M., Chen, Y. Q., Vinagre, B. M., Xue, D., & Feliu, V. (2010). Fractional-order systems and control: Fundamentals and applications. London: springer.MATH Concepcion, A. M., Chen, Y. Q., Vinagre, B. M., Xue, D., & Feliu, V. (2010). Fractional-order systems and control: Fundamentals and applications. London: springer.MATH
9.
Zurück zum Zitat Couceiro, M. S., Clemente, F. M., & Martins, F. M. L. (2013). Analysis of football player’ s motion in view of fractional calculus. Central European Journal of Physics, 11(6), 714–723. doi:10.2478/s11534-013-0258-5. Couceiro, M. S., Clemente, F. M., & Martins, F. M. L. (2013). Analysis of football player’ s motion in view of fractional calculus. Central European Journal of Physics, 11(6), 714–723. doi:10.​2478/​s11534-013-0258-5.
10.
Zurück zum Zitat Dzieliński, A., Sierociuk, D., & Sarwas, G. (2011). Some applications of fractional order calculus. Bulletin of the Polish Academy of Sciences: Technical Sciences, 58(4), 583–592. doi:10.2478/v10175-010-0059-6. Dzieliński, A., Sierociuk, D., & Sarwas, G. (2011). Some applications of fractional order calculus. Bulletin of the Polish Academy of Sciences: Technical Sciences, 58(4), 583–592. doi:10.​2478/​v10175-010-0059-6.
11.
Zurück zum Zitat El-Sayed, A., Nour, H., Elsaid, A., Matouk, A., & Elsonbaty, A. (2016). Dynamical behaviors, circuit realization, chaos control, and synchronization of a new fractional order hyperchaotic system. Applied Mathematical Modelling, 40(5), 3516–3534. doi:10.1016/j.apm.2015.10.010. El-Sayed, A., Nour, H., Elsaid, A., Matouk, A., & Elsonbaty, A. (2016). Dynamical behaviors, circuit realization, chaos control, and synchronization of a new fractional order hyperchaotic system. Applied Mathematical Modelling, 40(5), 3516–3534. doi:10.​1016/​j.​apm.​2015.​10.​010.
12.
Zurück zum Zitat Gao, Y. B., Sun, B. H., & Lu, G. P. (2013). Modified function projective lag synchronization of chaotic systems with disturbance estimations. Applied Mathematical Modelling, 37(7), 4993–5000.MathSciNetCrossRef Gao, Y. B., Sun, B. H., & Lu, G. P. (2013). Modified function projective lag synchronization of chaotic systems with disturbance estimations. Applied Mathematical Modelling, 37(7), 4993–5000.MathSciNetCrossRef
14.
Zurück zum Zitat Grosu, I. (1997). Robust synchronization. Physcial Review E, 56(3), 3709–3712.CrossRef Grosu, I. (1997). Robust synchronization. Physcial Review E, 56(3), 3709–3712.CrossRef
16.
Zurück zum Zitat Jackson, E. A., & Grosu, I. (1995). An open-plus-closed-loop (OPCL) control of complex dynamic systems. Physica D: Nonlinear Phenomena, 85(1), 1–9.MathSciNetCrossRefMATH Jackson, E. A., & Grosu, I. (1995). An open-plus-closed-loop (OPCL) control of complex dynamic systems. Physica D: Nonlinear Phenomena, 85(1), 1–9.MathSciNetCrossRefMATH
17.
Zurück zum Zitat Kapitaniak, M., Czolczynski, K., Perlikowski, P., Stefanski, A., & Kapitaniak, T. (2012). Synchronization of clocks. Physics Reports, 517(1–2), 1–69.CrossRefMATH Kapitaniak, M., Czolczynski, K., Perlikowski, P., Stefanski, A., & Kapitaniak, T. (2012). Synchronization of clocks. Physics Reports, 517(1–2), 1–69.CrossRefMATH
18.
Zurück zum Zitat Kareem, S. O., Ojo, K. S., & Njah, A. N. (2012). Function projective synchronization of identical and non-identical modified finance and Shimizu Morioka systems, 79(1), 71–79. doi:10.1007/s12043-012-0281-x. Kareem, S. O., Ojo, K. S., & Njah, A. N. (2012). Function projective synchronization of identical and non-identical modified finance and Shimizu Morioka systems, 79(1), 71–79. doi:10.​1007/​s12043-012-0281-x.
19.
Zurück zum Zitat Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141.CrossRef Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141.CrossRef
20.
Zurück zum Zitat Mahmoud, G. M., & Mahmoud, E. E. (2011). Modified projective lag synchronization of two nonidentical hyperchaotic complex nonlinear systems. International Journal of Bifurcation and Chaos, 21(08), 2369–2379. doi:10.1142/S0218127411029859.CrossRefMATH Mahmoud, G. M., & Mahmoud, E. E. (2011). Modified projective lag synchronization of two nonidentical hyperchaotic complex nonlinear systems. International Journal of Bifurcation and Chaos, 21(08), 2369–2379. doi:10.​1142/​S021812741102985​9.CrossRefMATH
21.
Zurück zum Zitat Mahmoud, G. M., Abed-Elhameed, T. M., & Ahmed, M. E. (2016). Generalization of combination—combination synchronization of chaotic n-dimensional fractional-order dynamical systems. Nonlinear Dynamics, 83(4), 1885–1893. doi:10.1007/s11071-015-2453-y. Mahmoud, G. M., Abed-Elhameed, T. M., & Ahmed, M. E. (2016). Generalization of combination—combination synchronization of chaotic n-dimensional fractional-order dynamical systems. Nonlinear Dynamics, 83(4), 1885–1893. doi:10.​1007/​s11071-015-2453-y.
22.
Zurück zum Zitat Mathiyalagan, K., Park, J. H., & Sakthivel, R. (2015). Exponential synchronization for fractional-order chaotic systems with mixed uncertainties. Complexity, 21(1), 114–125. doi:10.1002/cplx.21547. Mathiyalagan, K., Park, J. H., & Sakthivel, R. (2015). Exponential synchronization for fractional-order chaotic systems with mixed uncertainties. Complexity, 21(1), 114–125. doi:10.​1002/​cplx.​21547.
23.
Zurück zum Zitat Mohadeszadeh, M., & Delavari, H. (2015). Synchronization of fractional-order hyper-chaotic systems based on a new adaptive sliding mode control. International Journal of Dynamics and Control, 1–11. doi:10.1007/s40435-015-0177-y. Mohadeszadeh, M., & Delavari, H. (2015). Synchronization of fractional-order hyper-chaotic systems based on a new adaptive sliding mode control. International Journal of Dynamics and Control, 1–11. doi:10.​1007/​s40435-015-0177-y.
24.
Zurück zum Zitat Ogunjo, S. T. (2013). Increased and reduced order synchronization of 2D and 3D dynamical systems. International Journal of Nonlinear Science, 16(2), 105–112.MathSciNet Ogunjo, S. T. (2013). Increased and reduced order synchronization of 2D and 3D dynamical systems. International Journal of Nonlinear Science, 16(2), 105–112.MathSciNet
25.
Zurück zum Zitat Ogunjo, S. T., Adediji, A. T., & Dada, J. B. (2015). Investigating chaotic features in solar radiation over a tropical station using recurrence quantification analysis. Theoretical and Applied Climatology, 1–7. doi:10.1007/s00704-015-1642-4. Ogunjo, S. T., Adediji, A. T., & Dada, J. B. (2015). Investigating chaotic features in solar radiation over a tropical station using recurrence quantification analysis. Theoretical and Applied Climatology, 1–7. doi:10.​1007/​s00704-015-1642-4.
26.
Zurück zum Zitat Ojo, K., Njah, A., Olusola, O., & Omeike, M. (2014). Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique. Nonlinear Dynamics, 77(3), 583–595.MathSciNetCrossRefMATH Ojo, K., Njah, A., Olusola, O., & Omeike, M. (2014). Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique. Nonlinear Dynamics, 77(3), 583–595.MathSciNetCrossRefMATH
27.
Zurück zum Zitat Ojo, K., Njah, A., Olusola, O., & Omeike, M. (2014). Reduced order projective and hybrid projective combination-combination synchronization of four chaotic Josephson junctions. Journal of Chaos. Ojo, K., Njah, A., Olusola, O., & Omeike, M. (2014). Reduced order projective and hybrid projective combination-combination synchronization of four chaotic Josephson junctions. Journal of Chaos.
28.
Zurück zum Zitat Ojo, K., Njah, A., & Olusola, O. (2015). Compound-combination synchronization of chaos in identical and different orders chaotic systems. Archives of Control Sciences, 25(4), 463–490.MathSciNetCrossRefMATH Ojo, K., Njah, A., & Olusola, O. (2015). Compound-combination synchronization of chaos in identical and different orders chaotic systems. Archives of Control Sciences, 25(4), 463–490.MathSciNetCrossRefMATH
29.
Zurück zum Zitat Ojo, K., Njah, A., & Olusola, O. (2015). Generalized function projective combination-combination synchronization of chaos in third order chaotic systems. Chinese Journal of Physics, 53(3), l1–16. Ojo, K., Njah, A., & Olusola, O. (2015). Generalized function projective combination-combination synchronization of chaos in third order chaotic systems. Chinese Journal of Physics, 53(3), l1–16.
30.
Zurück zum Zitat Ojo, K. S., & Ogunjo, S. T. (2012). Synchronization of 4D Rabinovich hyperchaotic system for secure communication. Journal of Nigerian Association of Mathematical Physics, 21, 35–40. Ojo, K. S., & Ogunjo, S. T. (2012). Synchronization of 4D Rabinovich hyperchaotic system for secure communication. Journal of Nigerian Association of Mathematical Physics, 21, 35–40.
31.
Zurück zum Zitat Ojo, K. S., Njah, A., & Ogunjo, S. T. (2013). Comparison of backstepping and modified active control in projective synchronization of chaos in an extended Bonhoffer van der Pol oscillator. Pramana, 80(5), 825–835.CrossRef Ojo, K. S., Njah, A., & Ogunjo, S. T. (2013). Comparison of backstepping and modified active control in projective synchronization of chaos in an extended Bonhoffer van der Pol oscillator. Pramana, 80(5), 825–835.CrossRef
32.
Zurück zum Zitat Ojo, K. S., Ogunjo, S. T., & Williams, O. (2013). Mixed tracking and projective synchronization of 5D hyperchaotic system using active control. Cybernetics and Physics, 2, 31–36. Ojo, K. S., Ogunjo, S. T., & Williams, O. (2013). Mixed tracking and projective synchronization of 5D hyperchaotic system using active control. Cybernetics and Physics, 2, 31–36.
33.
Zurück zum Zitat Ojo, K. S., Njah, A., Ogunjo, S. T., & Olusola, O. I. (2014). Reduced order function projective combination synchronization of three Josephson junctions using backstepping technique. Nonlinear Dynamics and System Theory, 14(2), 119.MathSciNetMATH Ojo, K. S., Njah, A., Ogunjo, S. T., & Olusola, O. I. (2014). Reduced order function projective combination synchronization of three Josephson junctions using backstepping technique. Nonlinear Dynamics and System Theory, 14(2), 119.MathSciNetMATH
34.
Zurück zum Zitat Ojo, K. S., Njah, A. N. A., Ogunjo, S. T., Olusola, O. I., et al. (2014). Reduced order hybrid function projective combination synchronization of three Josephson junctions. Archives of Control Sciences, 24(1), 99–113. Ojo, K. S., Njah, A. N. A., Ogunjo, S. T., Olusola, O. I., et al. (2014). Reduced order hybrid function projective combination synchronization of three Josephson junctions. Archives of Control Sciences, 24(1), 99–113.
35.
Zurück zum Zitat Ojo, K. S., Ogunjo, S. T., Njah, A. N., & Fuwape, I. A. (2014). Increased-order generalized synchronization of chaotic and hyperchaotic systems, 84(1), 1–13. doi:10.1007/s12043-014-0835-1. Ojo, K. S., Ogunjo, S. T., Njah, A. N., & Fuwape, I. A. (2014). Increased-order generalized synchronization of chaotic and hyperchaotic systems, 84(1), 1–13. doi:10.​1007/​s12043-014-0835-1.
36.
Zurück zum Zitat Ouannas, A., Azar, A. T., & Vaidyanathan, S. (2016). A robust method for new fractional hybrid chaos synchronization. Mathematical Methods in the Applied Sciences, n/a–n/a. doi:10.1002/mma.4099. Ouannas, A., Azar, A. T., & Vaidyanathan, S. (2016). A robust method for new fractional hybrid chaos synchronization. Mathematical Methods in the Applied Sciences, n/a–n/a. doi:10.​1002/​mma.​4099.
37.
38.
Zurück zum Zitat Ramasubramanian, K., & Sriram, M. S. (2000). A comparative study of computation of lyapunov spectra with different algorithms. Physica D, 138(1–2), 72–86.MathSciNetCrossRefMATH Ramasubramanian, K., & Sriram, M. S. (2000). A comparative study of computation of lyapunov spectra with different algorithms. Physica D, 138(1–2), 72–86.MathSciNetCrossRefMATH
39.
40.
Zurück zum Zitat Strogatz, S. H. (1994). Nonlinear dynamics and chaos. Reading: Addison-Wesley. Strogatz, S. H. (1994). Nonlinear dynamics and chaos. Reading: Addison-Wesley.
41.
Zurück zum Zitat Wang, X., & Song, J. (2009). Synchronization of the fractional order hyperchaos lorenz system usin activstion feedback control. Communications in Nonlinear Science and Numerical Simulation, 14, 3351–3357.CrossRefMATH Wang, X., & Song, J. (2009). Synchronization of the fractional order hyperchaos lorenz system usin activstion feedback control. Communications in Nonlinear Science and Numerical Simulation, 14, 3351–3357.CrossRefMATH
42.
Zurück zum Zitat Wu, C. W., & Chua, L. O. (1994). A unified framework for synchronization and control of dynamical systems. International Journal of Bifurcation and Chaos, 4(4), 979–998.MathSciNetCrossRefMATH Wu, C. W., & Chua, L. O. (1994). A unified framework for synchronization and control of dynamical systems. International Journal of Bifurcation and Chaos, 4(4), 979–998.MathSciNetCrossRefMATH
Metadaten
Titel
Comparison of Three Different Synchronization Schemes for Fractional Chaotic Systems
verfasst von
S. T. Ogunjo
K. S. Ojo
I. A. Fuwape
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-50249-6_16

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