Abstract
In this paper, we investigate synchronization and its DSP implementation of fractional-order simplified Lorenz hyperchaotic systems by employing the Adomian decomposition method. The active controller and linear feedback controller are designed. Numerical simulation of the synchronized systems is carried out, and it is found that the synchronization phenomenon can be observed in both state variables and intermediate variables. Moreover, the synchronized systems are implemented in two TMS320F2-8335 DSP boards which are connected by a serial port and the output signals are exhibited by an oscilloscope. The experiment results show that the proposed implementation method works well on DSP.
Similar content being viewed by others
References
Li, C.G., Chen, G.R.: Chaos and hyperchaos in the fractional-order Rössler equations. Phys. A 341, 55–61 (2004)
Jia, H.Y., Chen, Z.Q., Xue, W.: Analysis and circuit implementation for the fractional-order Lorenz system. Acta Phys. Sin. 62, 140503 (2013)
Guo, Y.L., Qi, G.Y.: Topological horseshoe in a fractional-order Qi four-wing chaotic system. J. Appl. Anal. Comput. 5, 168–176 (2015)
Liu, W., Chen, K.: Chaotic behavior in a new fractional-order love triangle system with competition. J. Appl. Anal. Comput. 5, 103–113 (2015)
Zhang, C.X., Yu, S.M.: Generation of multi-wing chaotic attractor in fractional order system. Chaos Solitons Fractals 44, 845–850 (2011)
Xu, B.B., Chen, D.Y., Zhang, H., et al.: Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit. Nonlinear Dyn. 81, 1263–1274 (2015)
Chen, D., Zhao, W., Sprott, J.C., et al.: Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization. Nonlinear Dyn. 73, 1495–1505 (2013)
Zhang, S., Yu, Y., Wen, G., et al.: Lag-generalized synchronization of time-delay chaotic systems with stochastic perturbation. Mod. Phys. Lett. B 30, 1550263 (2016)
Bhalekar, S., Daftardar-Gejji, V.: Synchronization of different fractional order chaotic systems using active control. Commun. Nonlinear Sci. Numer. Simul. 15, 3536–3546 (2013)
Chen, D.Y., Zhang, R., Sprott, J.C., et al.: Synchronization between integer-order chaotic systems and a class of fractional-order chaotic system based on fuzzy sliding mode control. Chaos 22, 1549-156 (2012)
Tavazoei, M.S., Haeri, M.: Synchronization of chaotic fractional-order systems via active sliding mode controller. Phys. A 387, 57–70 (2008)
Gammoudi, I.E., Feki, M.: Synchronization of integer order and fractional order Chua’s systems using robust observer. Commun. Nonlinear Sci. Numer. Simul. 18, 625–638 (2013)
Zhang, R.X., Yang, S.P.: Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation. Chin. Phys. B 18, 3295–3303 (2009)
Chen, D., Wu, C., Iu, H.H.C., et al.: Circuit simulation for synchronization of a fractional-order and integer-order chaotic system. Nonlinear Dyn. 73, 1671–1686 (2013)
Li, H., Liao, X., Luo, M.: A novel non-equilibrium fractional-order chaotic system and its complete synchronization by circuit implementation. Nonlinear Dyn. 68, 137–149 (2012)
Bing, L.V., Zhu, C.J.: Coupled generalized projective synchronization of the fractional-order hyperchaotic system and its application in secure communication. Nonlinear Anal. Real World Appl. 13, 1441–1450 (2012)
Lin, Z., Yu, S., Lu, J., et al.: Design and ARM-embedded implementation of a chaotic map-based real-time secure video communication system. IEEE Trans. Circuits Syst. Video Technol. 25, 1203–1216 (2015)
Charef, A., Sun, H.H., Tsao, Y.Y., et al.: Fractal system as represented by singularity function. IEEE Trans. Autom. Control 37, 1465–1470 (1992)
Sun, H., Abdelwahab, A., Onaral, B.: Linear approximation of transfer function with a pole of fractional power. IEEE Trans. Autom. Control 29, 441–444 (1984)
Penaud, S., Guittard, J., Bouysse, P.: DSP implementation of self-synchronised chaotic encoder decoder. Electron. Lett. 36, 365–366 (2000)
Lin, J.S., Huang, C.F., Liao, T.L., et al.: Design and implementation of digital secure communication based on synchronized chaotic systems. Digit. Signal Process. 20, 229–237 (2010)
Wang, Q.X., Yu, S.M., Guyeux, C.: Study on a new chaotic bitwise dynamical system and its FPGA implementation. Chin. Phys. B 24, 184–191 (2015)
Wang, H.H., Sun, K.H., He, S.B.: Characteristic analysis and DSP realization of fractional-order simplified Lorenz system based on Adomian decomposition method. Int. J. Bifurc. Chaos 25, 1550085 (2015)
He, S.B., Sun, K.H., Wang, H.H.: Complexity analysis and DSP implementation of the fractional-order Lorenz hyperchaotic system. Entropy 17, 8299–8311 (2015)
Wang, H.H., Sun, K.H., He, S.B.: Dynamic analysis and implementation of a digital signal processor of a fractional-order Lorenz–Stenflo system based on the Adomian decomposition method. Phys. Scr. 90, 015206 (2015)
Caponetto, R., Fazzino, S.: An application of Adomian decomposition for analysis of fractional-order chaotic systems. Int. J. Bifurc. Chaos 72, 301–309 (2013)
Gorenflo, R., Mainardi, F.: Fractional calculus: integral and differential equations of fractional order. Mathematics 49, 277–290 (2008)
Donato, C., Giuseppe, G.: Bifurcation and chaos in the fractional-order Chen system via a time-domain approach. Int. J. Bifurc. Chaos 18, 1845–1863 (2016)
Sun, K.H., Liu, X., Zhu, C.X.: Dynamics of a strengthened chaotic system and its circuit implementation. Chin. J. Electron. 23, 353–356 (2014)
He, S.B., Sun, K.H., Wang, H.H.: Solution and dynamics analysis of a fractional-order hyperchaotic system. Math. Methods Appl. Sci. 39, 2965–2973 (2016)
Acknowledgements
This work was supported by the Startup Foundation for Doctoral research (No. E07016048)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
He, S., Sun, K., Wang, H. et al. Generalized synchronization of fractional-order hyperchaotic systems and its DSP implementation. Nonlinear Dyn 92, 85–96 (2018). https://doi.org/10.1007/s11071-017-3907-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-017-3907-1