89
Views
10
CrossRef citations to date
0
Altmetric
Original Article

Multi-switching combination synchronization of different fractional-order non-linear dynamical systems

&
Pages 254-261 | Received 05 Mar 2017, Accepted 02 Dec 2017, Published online: 13 Mar 2018

References

  • Podlubny I. Fractional differential equations. New York (NY): Academic Press; 1999.
  • Hilfer R, editor. Applications of fractional calculus in physics. World Scientific; 2000.
  • Caponetto R, Trujillo JJ, Machado JAT. Theory and applications of fractional order systems 2016. Mathematical Problems in Engineering; 2016.
  • Lazopoulos KA, Karaoulanis D, Lazopoulos AK. On fractional modelling of viscoelastic mechanical systems. Mech Res Commun. 2016;78:1–5.10.1016/j.mechrescom.2016.10.002
  • Bhrawy AH, Zaky MA. Shifted fractional-order Jacobi orthogonal functions: Application to a system of fractional differential equations. Appl Math Model. 2016;40(2):832–845.10.1016/j.apm.2015.06.012
  • Agarwal RP, El-Sayed AM, Salman SM. Fractional-order Chuas system: discretization, bifurcation and chaos. Adv Diff Equ. 2013;2013(1):1.
  • Li C, Chen G. Chaos and hyperchaos in the fractional-order Rössler equations. Phys A. 2004;341:55–61.10.1016/j.physa.2004.04.113
  • Li C, Peng G. Chaos in Chen’s system with a fractional order. Chaos, Solitons Fractals. 2004;22(2):443–450.10.1016/j.chaos.2004.02.013
  • Deng WH, Li CP. Chaos synchronization of the fractional Lü system. Phys A. 2005;353:61–72.10.1016/j.physa.2005.01.021
  • Ge ZM, Ou CY. Chaos in a fractional order modified Duffing system. Chaos, Solitons Fractals. 2007;34(2):262–291.10.1016/j.chaos.2005.11.059
  • Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys Rev Lett. 1990;64(8):821–824.10.1103/PhysRevLett.64.821
  • Asheghan MM, Beheshti MTH, Tavazoei MS. Robust synchronization of perturbed Chens fractional-order chaotic systems. Commun Nonlinear Sci Numer Simul. 2011;16(2):1044–1051.10.1016/j.cnsns.2010.05.024
  • Chen L, Wu R, He Y, et al. Adaptive slidingmode control for fractional-order uncertain linear systems with nonlinear disturbances. Nonlinear Dyn. 2015;80(1–2):51–58.10.1007/s11071-014-1850-y
  • Khan A, Bhat MA. Hyperchaotic analysis and adaptive projective synchronization of nonlinear dynamical system. Comput Math Model. 2017;1–14.
  • Khan A. Hybrid function projective synchronization of chaotic systems via adaptive control. Int J Dyn Control. 2016;1–8.
  • Khan A, Bhat MA. Hybrid projective synchronization of fractional order chaotic systems with fractional order in the interval (1, 2). Nonlinear Dyn Syst Theory. 2016;16(4):350–365.
  • Masoller C, nindexDamianDamiaan HZ. Anticipated synchronization in coupled chaotic maps with delays. Phys A. 2001;300(3–4):359–366.10.1016/S0378-4371(01)00362-4
  • Khan A, Bhat MA. Analysis and projective synchronization of new 4D hyperchaotic system. J Uncertain Syst. 2017;11(4):257–268.
  • Mainieri R, Rehacek J. Projective synchronization in three-dimensional chaotic systems. Phys Rev Lett. 1999;82(15):3042–3045.10.1103/PhysRevLett.82.3042
  • Khan A, Bhat MA. Hyper-chaotic analysis and adaptive multi-switching synchronization of a novel asymmetric nonlinear dynamical system. Int J Dyn Control. 2016;1–11.
  • Vaidyanathan S, Azar AT. Generalized projective synchronization of a novel hyperchaotic four-wing system via adaptive control method. In: Advances in chaos theory and intelligent control. Springer; 2016. p. 275–296.10.1007/978-3-319-30340-6
  • Runzi L, Yinglan W, Shucheng D. Combination synchronization of three classic chaotic systems using active backstepping design. Chaos Interdisciplinary J Nonlinear Sci. 2011;21(4):043114.
  • Runzi L, Yinglan W. Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication. Chaos Interdisciplinary J Nonlinear Sci. 2012;22(2):023109.
  • Sun J, Shen Y, Yin Q, et al. Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos Interdisciplinary J Nonlinear Sci. 2013;23(1):013140.
  • Sun J, Yin Q, Shen Y. Compound synchronization for four chaotic systems of integer order and fractional order. EPL. 2014;106(4):40005.10.1209/0295-5075/106/40005
  • Wu A, Zhang J. Compound synchronization of fourth-order memristor oscillator. Adv Differ Equ. 2014;2014(1):1.
  • Sun J, Shen Y, Zhang G, et al. Combination–combination synchronization among four identical or different chaotic systems. Nonlinear Dyn. 2013;73(3):1211–1222.10.1007/s11071-012-0620-y
  • Khan A, Bhat MA. Multi-switching combination–combination synchronization of non‐identical fractional order chaotic systems. Math Methods Appl Sci. 2017. DOI: 10.1002/mma.4416.
  • Zhang B, Deng F. Double-compound synchronization of six memristor-based Lorenz systems. Nonlinear Dyn. 2014;77(4):1519–1530.10.1007/s11071-014-1396-z
  • Ojo KS, Njah AN, Olusola OI. Compoundcombination synchronization of chaos in identical and different orders chaotic systems. Arch Control Sci. 2015;25(4):463–490.
  • Ucar A, Lonngren KE, Bai EW. Multi-switching synchronization of chaotic systems with active controllers. Chaos, Solitons Fractals. 2008;38(1):254–262.10.1016/j.chaos.2006.11.041
  • Vincent UE, Saseyi AO, McClintock PV. Multiswitching combination synchronization of chaotic systems. Nonlinear Dyn. 2015;80(1–2):845–854.10.1007/s11071-015-1910-y
  • Matignon D. Stability results for fractional differential equations with applications to control processing. Comput Eng Syst Appl. 1996;2:963–968.
  • Yu Y, Li HX, Wang S, et al. Dynamic analysis of a fractional-order Lorenz chaotic system. Chaos, Solitons Fractals. 2009;42(2):1181–1189.10.1016/j.chaos.2009.03.016
  • Li C, Chen G. Chaos in the fractional order Chen system and its control. Chaos, Solitons Fractals. 2004;22(3):549–554.10.1016/j.chaos.2004.02.035

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.