Page 687 - Mathematical Techniques of Fractional Order Systems

658 Mathematical Techniques of Fractional Order Systems

Chen, D., Zhang, R., Liu, X., Ma, X., 2014. Fractional order Lyapunov stability theorem and its
applications in synchronization of complex dynamical networks. Commun. Nonlinear Sci.
Numer. Simul. 19 (12), 4105 4121.
Chen, X.R., Liu, C.X., 2012. Chaos synchronization of fractional order unified chaotic system
via nonlinear control. Int. J. Mod. Phys. B 25 (3), 407 415.
Das, S., Pan, I., Das, S., 2016. Effect of random parameter switching on commensurate fractional
order chaotic systems. Chaos, Solitons Fractals 91 (2016), 157 173.
Deng, W.H., Li, C.P., 2005. Chaos synchronization of the fractional Lu ¨ system. Phys. A 353 (1-
4), 61 72.
Devaney, R.L., 1989. An Introduction to Chaotic Dynamical System. Addison Wesley Publ.
Comp, Redwood City, CA.
Diethelm, K., Ford, N.J., Freed, A.D., 2002. A predictor-corrector approach for the numerical
solution of fractional differential equations. Nonlinear Dynam. 29 (1-4), 3 22.
Dorca ´k, L., 1994. Numerical models for the simulation of the fractional-order control systems.
UEF-04-94, The Academy of Sciences, Inst. of Experimental Physic, Kosice, Slovakia
Republic, 12p.
Eckmann, J.P., Kamphorst, S.O., Ruelle, D., 1987. Recurrence plots of dynamical systems.
Europhys. Lett. 4 (9), 973 977.
Grassi, G., Ouannas, A., Azar, A.T., Radwan, A.G., Volos, C., Pham, V.T., et al., 2017. Chaos
synchronisation of continuous systems via scalar signal. The 6th International Conference
on Modern Circuits and Systems Technologies (MOCAST), Thessaloniki Greece, 4-6 May.
Grigorenko, I., Grigorenko, E., 2003. Chaotic dynamics of the fractional Lorenz system. Phys.
Rev. Lett. 91 (3), 034101 034104.
Huang, L., Xin, F., 2010. Generalized synchronization between different fractional-order chaotic
systems based on nonlinear feedback. IEEE, Fifth International Conference on Bio-Inspired
Computing: Theories and Applications (BIC-TA), 10141 1017.
Kantz, H., Schreiber, T., 1997. Nonlinear time series analysis. Cambridge Nonlinear Science
Series 7. Cambridge University Press, Cambridge, UK, ISBN: 0521 551447.
Li, C., Chen, G., 2004. Chaos and hyperchaos in the fractional-order Ro ¨ssler equations. Phys. A
341 (1-4), 55 61.
Li, C., Deng, W., 2006. Chaos synchronization of fractional-order differential systems. Int. J.
Modern Phys. B 20 (7), 791 803.
Li, C., Yan, J., 2007. The synchronization of three fractional differential systems. Chaos Solitons
Fractals 32 (2), 751 757.
Li, C.D., Chen, Q., Huang, T., 2008a. Coexistence of anti-phase and complete synchronization
in coupled Chen system via a single variable. Chaos Solitons Fractals 38 (2), 461 464.
Li, G.H., 2007. Modified projective synchronization of chaotic system. Chaos Solitons Fractals
32 (5), 1786 1790.
Li, W.L., Chen, X.Q., Shen, Z.P., 2008b. Anti-synchronization of two different chaotic systems.
Phys. A 387 (14), 3747 3757.
Liu, C., Liu, L., Liu, T., 2009. A novel three-dimensional autonomous chaos system. Chaos
Solitons Fractals 39 (4), 1950 1958.
Lu, J.F., 2008. Generalized (complete, lag, anticipated) synchronization of discrete-time chaotic
systems. Commun. Nonlinear Sci. Numer. Simul. 13 (9), 1851 1859.
Lu, J.G., 2005. Chaotic dynamics and synchronization of fractional-order Arneodo’s systems.
Chaos Solitons Fractals 26 (4), 1125 1133.
Lu, J.G., Chen, G., 2006. A note on the fractional-order Chen system. Chaos Solitons Fractals
27 (3), 685 688.