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Response to the comments on “Adaptive synchronization of fractional-order chaotic systems via a single driving variable”. (English) Zbl 1242.93097

Summary: This paper is a response to the comment by M.P. Aghababa [Nonlinear Dyn., doi:''10.1007/s11071-011-0216-y'' (2011; Zbl 1242.93026)]. Some ideas are proposed to rebut the Comments.

MSC:

93C95 Application models in control theory
34H10 Chaos control for problems involving ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations

Citations:

Zbl 1242.93026
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References:

[1] Aghababa, M.P.: Comments on ”Adaptive synchronization of fractional-order chaotic systems via a single driving variable”. Nonlinear Dyn. (2011). doi: 10.1007/s11071-011-0216-y · Zbl 1243.93022
[2] Zhang, R., Yang, S.: Adaptive synchronization of fractional-order chaotic systems via a single driving variable. Nonlinear Dyn. (2011). doi: 10.1007/s11071-011-9944-2 · Zbl 1242.93030
[3] Razmjou, E.G., Ranjbar, A., Rahmani, Z., Ghaderi, R.: Robust synchronization and parameter identification of fractional-order unified chaotic system. In: 3rd Conference on Nonlinear Science and Complexity, Ankara, Turkey (2010)
[4] Si-Ammour, A., Djennoune, S., Bettaye, M.: A sliding mode control for linear fractional system with input and state delays. Commun. Nonlinear Sci. Numer. Simul. 14, 2310–2318 (2009) · Zbl 1221.93048
[5] Balochian, S., Khaki Sedigh, A., Zare, A.: Stabilization of multi-input hybrid fractional-order systems with state delay. ISA Trans. 50, 21–27 (2011) · Zbl 1221.93041
[6] Yin, C., Zhong, S.-m., Chen, W.-f.: Design of sliding mode controller for a class of fractional-order chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 17, 356–366 (2012) · Zbl 1248.93041
[7] Dadras, S., Reza Momeni, H.: Control of a fractional-order economical system via sliding mode. Physica A 389, 2434–2442 (2010)
[8] Aghababa, M.P.: Comments on ”Design of sliding mode controller for a class of fractional-order chaotic systems”. Commun. Nonlinear Sci. Numer. Simul. (2011). doi: 10.1016/j.cnsns.2011.04.024
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