Cover
Vol. 17 No. 1 (2021)

Published: June 30, 2021

Pages: 116-124

Original Article

New Fractional Order Chaotic System: Analysis, Synchronization, and it’s Application

Zain-Aldeen S. A. Rahman 1 Basil Hani Jasim Yasir I. A. Al-Yasir 2
1Dept. of Electrical Techniques Technical Institute / Qurna, Southern Technical University
2School of Electrical Engineering and Computer Science, Faculty of Engineering and Informatics, University of Bradford,
History
  • Received: March 19, 2021
  • Revised: April 27, 2021
  • Accepted: April 27, 2021
  • Available Online: May 10, 2021
DOI

https://doi.org/10.37917/ijeee.17.1.14

Abstract

In this paper, a new nonlinear dynamic system, new three-dimensional fractional order complex chaotic system, is presented. This new system can display hidden chaotic attractors or self-excited chaotic attractors. The Dynamic behaviors of this system have been considered analytically and numerically. Different means including the equilibria, chaotic attractor phase portraits, the Lyapunov exponent, and the bifurcation diagrams are investigated to show the chaos behavior in this new system. Also, a synchronization technique between two identical new systems has been developed in master- slave configuration. The two identical systems are synchronized quickly. Furthermore, the master-slave synchronization is applied in secure communication scheme based on chaotic masking technique. In the application, it is noted that the message is encrypted and transmitted with high security in the transmitter side, in the other hand the original message has been discovered with high accuracy in the receiver side. The corresponding numerical simulation results proved the efficacy and practicability of the developed synchronization technique and its application

Keywords

References

  1. V. T. Pham, S. Vaidyanathan, C. K. Volos, and S. Jafari, “Hidden attractors in a chaotic system with an exponential nonlinear term,” Eur. Phys. J. Spec. Top., vol. 224, no. 8, pp. 1507–1517, 2015.
  2. B. H. Jasim, K. H. Hassan, and K. M. Omran, “A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation.,” Int. J. Electr. Comput. Eng., vol. 11, no. 3, 2021.
  3. A. Bayani, K. Rajagopal, A. J. M. Khalaf, S. Jafari, G. D. Leutcho, and J. Kengne, “Dynamical analysis of a new multistable chaotic system with hidden attractor: Antimonotonicity, coexisting multiple attractors, and offset boosting,” Phys. Lett. A, vol. 383, no. 13, pp. 1450– 1456, 2019. Rahman, Jasim & Al-Yasir | 123
  4. V.-T. Pham, S. Vaidyanathan, C. Volos, and T. Kapitaniak, Nonlinear dynamical systems with self-excited and hidden attractors, vol. 133. Springer, 2018.
  5. F. R. Tahir, S. Jafari, V.-T. Pham, C. Volos, and X. Wang, “A novel no-equilibrium chaotic system with multiwing butterfly attractors,” Int. J. Bifurc. Chaos, vol. 25, no. 04, p. 1550056, 2015.
  6. G. A. Leonov, N. V Kuznetsov, and T. N. Mokaev, “Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion,” Eur. Phys. J. Spec. Top., vol. 224, no. 8, pp. 1421–1458, 2015.
  7. G. A. Leonov, N. V Kuznetsov, M. A. Kiseleva, E. P. Solovyeva, and A. M. Zaretskiy, “Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor,” Nonlinear Dyn., vol. 77, no. 1–2, pp. 277–288, 2014.
  8. B. R. Andrievsky, N. V Kuznetsov, G. A. Leonov, and A. Y. Pogromsky, “Hidden oscillations in aircraft flight control system with input saturation,” IFAC Proc. Vol., vol. 46, no. 12, pp. 75–79, 2013.
  9. G. A. Leonov and N. V Kuznetsov, “Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits,” Int. J. Bifurc. Chaos, vol. 23, no. 01, p. 1330002, 2013.
  10. L. Moysis, C. Volos, V.-T. Pham, S. Goudos, I. Stouboulos, and M. K. Gupta, “Synchronization of a chaotic system with line equilibrium using a descriptor observer for secure communication,” in 2019 8th International Conference on Modern Circuits and Systems Technologies (MOCAST), 2019, pp. 1–4.
  11. F. Nazarimehr, V.-T. Pham, K. Rajagopal, F. E. Alsaadi, T. Hayat, and S. Jafari, “A New Imprisoned Strange Attractor,” Int. J. Bifurc. Chaos, vol. 29, no. 13, p. 1950181, 2019.
  12. A. Ahmadi, X. Wang, F. Nazarimehr, F. E. Alsaadi, F. E. Alsaadi, and V.-T. Pham, “Coexisting infinitely many attractors in a new chaotic system with a curve of equilibria: Its extreme multi-stability and Kolmogorov– Sinai entropy computation,” Adv. Mech. Eng., vol. 11, no. 11, p. 1687814019888046, 2019.
  13. F. Yang, J. Mou, C. Ma, and Y. Cao, “Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application,” Opt. Lasers Eng., vol. 129, p. 106031, 2020.
  14. M. S. Tavazoei and M. Haeri, “Regular oscillations or chaos in a fractional order system with any effective dimension,” Nonlinear Dyn., vol. 54, no. 3, pp. 213–222, 2008.
  15. A.-B. A. Al-Hussein and F. R. Tahir, “A New Model For Endocrine Glucose-Insulin Regulatory System,” Iraqi J. Electr. Electron. Eng., vol. 16, no. 1, 2020.
  16. F. N. Ayoob, F. R. Tahir, and K. M. Abdul-Hassan, “Bifurcations and Chaos in Current-Driven Induction Motor,” Iraqi J. Electr. Electron. Eng., vol. 15, no. 2– 2019, 2019.
  17. B. H. Jasim, M. T. Rashid, and K. M. Omran, “Synchronization and tracking control of a novel 3 dimensional chaotic system,” Iraqi J. Electr. Electron. Eng., no. 3RD, 2020.
  18. K. Rajagopal, F. Nazarimehr, A. Karthikeyan, A. Srinivasan, and S. Jafari, “CAMO: Self-Excited and Hidden Chaotic Flows,” Int. J. Bifurc. Chaos, vol. 29, no. 11, p. 1950143, 2019.
  19. C. Ma, J. Mou, J. Liu, F. Yang, H. Yan, and X. Zhao, “Coexistence of multiple attractors for an incommensurate fractional-order chaotic system,” Eur. Phys. J. Plus, vol. 135, no. 1, pp. 1–21, 2020.
  20. S. Jafari, J. C. Sprott, and F. Nazarimehr, “Recent new examples of hidden attractors,” Eur. Phys. J. Spec. Top., vol. 224, no. 8, pp. 1469–1476, 2015.
  21. S. Jafari, V.-T. Pham, S. M. R. H. Golpayegani, M. Moghtadaei, and S. T. Kingni, “The relationship between chaotic maps and some chaotic systems with hidden attractors,” Int. J. Bifurc. Chaos, vol. 26, no. 13, p. 1650211, 2016.
  22. I. Pan and S. Das, Intelligent fractional order systems and control: an introduction, vol. 438. Springer, 2012.
  23. P. Muthukumar and P. Balasubramaniam, “Feedback synchronization of the fractional order reverse butterfly- shaped chaotic system and its application to digital cryptography,” Nonlinear Dyn., vol. 74, no. 4, pp. 1169– 1181, 2013.
  24. Z. Rahman, H. AL-Kashoash, S. Ramadhan, and Y. Al- yasir, “adaptive control synchronization of a novel Menristive chaotic system for secure communication application,” Inventions, vol. 10, pp. 1–11, 2019.
  25. A. Karthikeyan, K. Rajagopal, V. Kamdoum Tamba, G. Adam, and A. Srinivasan, “A Simple Chaotic Wien Bridge Oscillator with a Fractional-Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability,” Complexity, vol. 2021, 2021.
  26. F. Nian, X. Liu, and Y. Zhang, “Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances,” Chaos, Solitons & Fractals, vol. 116, pp. 22–28, 2018.
  27. C. Huang and J. Cao, “Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system,” Phys. A Stat. Mech. its Appl., vol. 473, pp. 262–275, 2017.
  28. O. Mofid, S. Mobayen, and M. Khooban, “Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems,” Int. J. Adapt. Control Signal Process., vol. 33, no. 3, pp. 462–474, 2019.
  29. T. Ma, W. Luo, Z. Zhang, and Z. Gu, “Impulsive synchronization of fractional-order chaotic systems with actuator saturation and control gain error,” IEEE Access, vol. 8, pp. 36113–36119, 2020.
  30. S. Keyong, B. Ruixuan, G. Wang, W. Qiutong, and Z. Yi, “Passive Synchronization Control for Integer-order Chaotic Systems and Fractional-order Chaotic Systems,” in 2019 Chinese Control Conference (CCC), 2019, pp. 1115–1119.
  31. J. Liu, Z. Wang, M. Shu, F. Zhang, S. Leng, and X. Sun, “Secure communication of fractional complex chaotic systems based on fractional difference function synchronization,” Complexity, vol. 2019, 2019.
  32. H. Jia, Z. Guo, G. Qi, and Z. Chen, “Analysis of a four- Rahman, Jasim & Al-Yasir wing fractional-order chaotic system via frequency- domain and time-domain approaches and circuit implementation for secure communication,” Optik (Stuttg)., vol. 155, pp. 233–241, 2018.
  33. S. Djennoune, M. Bettayeb, and U. M. Al-Saggaf, “Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication,” Int. J. Appl. Math. Comput. Sci., vol. 29, no. 1, pp. 179–194, 2019.
  34. A. Durdu and Y. Uyaroğlu, “The shortest synchronization time with optimal fractional order value using a novel chaotic attractor based on secure communication,” Chaos, Solitons & Fractals, vol. 104, pp. 98–106, 2017.
  35. D. Baleanu and A. Fernandez, “On fractional operators and their classifications,” Mathematics, vol. 7, no. 9, p. 830, 2019.
  36. H. Sun, Y. Zhang, D. Baleanu, W. Chen, and Y. Chen, “A new collection of real world applications of fractional calculus in science and engineering,” Commun. Nonlinear Sci. Numer. Simul., vol. 64, pp. 213–231, 2018.
  37. M. Alaeiyan, M. R. Farahani, and M. K. Jamil, “Computation of the fifth geometric-arithmetic index for polycyclic aromatic hydrocarbons PaHk,” Appl. Math. Nonlinear Sci., vol. 1, no. 1, pp. 283–290, 2016.
  38. X. Song, S. Song, and B. Li, “Adaptive synchronization of two time-delayed fractional-order chaotic systems with different structure and different order,” Optik (Stuttg)., vol. 127, no. 24, pp. 11860–11870, 2016.
  39. N. Debbouche, S. Momani, A. Ouannas, G. Grassi, Z. Dibi, and I. M. Batiha, “Generating Multidirectional Variable Hidden Attractors via Newly Commensurate and Incommensurate Non-Equilibrium Fractional-Order Chaotic Systems,” Entropy, vol. 23, no. 3, p. 261, 2021.
  40. M.-F. Danca and N. Kuznetsov, “Matlab code for Lyapunov exponents of fractional-order systems,” Int. J. Bifurc. Chaos, vol. 28, no. 05, p. 1850067, 2018.
  41. S. Vaidyanathan and C. Volos, Advances and applications in chaotic systems, vol. 636. Springer, 2016.
  42. H. Jahanshahi, A. Yousefpour, J. M. Munoz-Pacheco, S. Kacar, V.-T. Pham, and F. E. Alsaadi, “A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption,” Appl. Math. Comput., vol. 383, p. 125310, 2020.
  43. Z. Peng et al., “Dynamic analysis of seven-dimensional fractional-order chaotic system and its application in encrypted communication,” J. Ambient Intell. Humaniz. Comput., pp. 1–19, 2020.
  44. M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics, vol. 9, no. 3, pp. 151–162, 2015.