Dynamics and circuit simulation of a fractional-order hyperchaotic system

Document Type : Article

Authors

1 University of Carthage, National Institute of Applied Sciences and Technology, INSAT, Centre Urbain Nord, BP676, 1080 Tunis Cedex, Tunisia

2 Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, P.O. Box 15875-4413, Iran

Abstract

A hyperchaotic system with fractional terms and fractional-order derivatives
is investigated in this paper. Simulations show that different attractors such
as equilibrium point, limit cycle and hyperchaotic attractor can be generated
by the system. Circuit of fractional-order integrator is designed and it is used
to implement the circuit of the studied system. The circuit implementation
of the studied system proofs its feasibility. A hyperchaotic system with fractional terms and fractional-order derivatives
is investigated in this paper. Simulations show that different attractors such
as equilibrium point, limit cycle and hyperchaotic attractor can be generated
by the system. Circuit of fractional-order integrator is designed and it is used
to implement the circuit of the studied system. The circuit implementation
of the studied system proofs its feasibility.

Keywords


References:
1. Podlubny, I. "Fractional-order systems and pid -controllers", IEEE Trans. Automat. Contr., 44(1), pp. 208-214 (1999).
2. Diethelm, K., The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer-Verlag Berlin Heidelberg, Germany (2010).
3. Petras, I., Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer-Verlag Berlin Heidelberg, Germany (2011).
4. Vastarouchas, C., Psychalinos, C., and Elwakil, A.S. "Fractional-order model of a commercial ear simulator", 2018 IEEE Int. Symp. Circuits Syst., Florence, Italy, pp. 1-4 (2018).
5. Lassoued, A. and Boubaker, O. "On new chaotic and hyperchaotic systems: A literature survey", Nonlinear Anal-Model, 21(6), pp. 770-789 (2016).
6. Ran, J. "Discrete chaos in a novel two-dimensional fractional chaotic map", Adv. Differ. Equ., 2018, pp. 294:1-12 (2018).
7. Li, H., Liao, X., and Luo, M. "A novel non-equilibrium fractional-order chaotic system and its complete synchronization by circuit implementation", Nonlinear Dyn., 68(1-2), pp. 137-149 (2012).
8. Buscarino, A., Fortuna, L., Frasca, M., et al. "A chaotic circuit based on hewlett-packard memristor", Chaos, 22(2), pp. 023136:1-9 (2012).
9. Buscarino, A., Fortuna, L., and Frasca, M. "The jerk dynamics of chua's circuit", Int. J. Bifurc. Chaos, 24(06), pp. 1450085:1-10 (2014).
10. Bao, B., Wang, N., Chen, M., et al. "Inductorfree simplified chua's circuit only using two-op-ampbased realization", Nonlinear Dyn., 84(2), pp. 511-525 (2016).
11. Prakash, P., Singh, J.P., and Roy, B. "Fractionalorder memristor-based chaotic jerk system with no equilibrium point and its fractional-order backstepping control", IFAC-PapersOnLine, 51(1), pp. 1-6 (2018).
12. Vaidyanathan, S., Sambas, A., and Mamat, M. "Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption", Int. J. Model. Identif. Control, 28(2), pp. 153-166 (2017).
13. Podlubny, I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Academic press, New York, USA (1998).
14. Jian-Bing, H. and Ling-Dong, Z. "Stability theorem and control of fractional systems", Acta. Phys. Sin., 62(24), pp. 240504:1-7 (2013).
15. Diethelm, K. and Ford, N.J. "Analysis of fractional differential equations", J. Math. Anal. Appl., 265(2), pp. 229-248 (2002).
16. Lassoued, A. and Boubaker, O. "Dynamic analysis and circuit design of a novel hyperchaotic system with fractional-order terms", Complexity, 2017, pp. 1-10 (2017).
17. Danca, M. and Kuznetsov, N. "Matlab code for lyapunov exponents of fractional-order systems", Int. J. Bifurc. Chaos, 28(05), pp. 1850067:1-14 (2018).
18. Charef, A., Sun, H., Tsao, Y., and Onaral, B. "Fractal system as represented by singularity function", IEEE Trans. Automat. Contr., 37(9), pp. 1465-1470 (1992).
19. Ahmad, W.M. and Sprott, J. "Chaos in fractionalorder autonomous nonlinear systems", Chaos Soliton. Fract., 16(2), pp. 339-351 (2003).
20. Ruo-Xun, Z. and Shi-Ping, Y. "Chaos in fractionalorder generalized lorenz system and its synchronization circuit simulation", Chin. Phys. B, 18(8), pp. 3295- 3303 (2009).
Volume 30, Issue 2
Transactions on Computer Science & Engineering and Electrical Engineering (D)
March and April 2023
Pages 507-517
  • Receive Date: 18 January 2020
  • Revise Date: 17 March 2021
  • Accept Date: 19 July 2021