Research Article
BibTex RIS Cite

Year 2025, Volume: 7 Issue: 2, 117 - 124, 31.07.2025
https://doi.org/10.51537/chaos.1633880

Abstract

References

  • Abd El-Maksoud, A. J., A. A. Abd El-Kader, B. G. Hassan, M. A. Abdelhamed, N. G. Rihan, et al., 2018 FPGA implementation of fractional-order Chua’s chaotic system. In 2018 7th international conference on modern circuits and systems technologies (MOCAST), (pp. 1–4), IEEE.
  • Abd El-Maksoud, A. J., A. A. Abd El-Kader, B. G. Hassan, N. G. Rihan, M. F. Tolba, et al., 2019 FPGA implementation of sound encryption system based on fractional-order chaotic systems. Microelectronics Journal 90: 323–335.
  • Adhikary, A., S. Sen, and K. Biswas, 2016 Practical realization of tunable fractional order parallel resonator and fractional order filters. IEEE Transactions on Circuits and Systems I: Regular Papers 63(8): 1142–1151.
  • Ahmad, W., R. El-Khazali, and A. S. Elwakil, 2001 Fractional-order Wien-bridge oscillator. Electronics Letters 37(18): 1110–1112.
  • Boudjerida, N., M. S. Abdelouahab, R. Lozi, 2022 Modified projective synchronization of fractional-order hyperchaotic memristorbased Chua’s circuit. Journal of Innovative Applied Mathematics and Computational Sciences 2(3): 69–85.
  • A. Charef, H. H. Sun, Y. Y. Tsao, and B. Onaral, 1992 Fractal system as represented by singularity function. IEEE Transactions on automatic Control 37(9): 1465–1470.
  • H. Chen, F. Holland, and M. Stynes, 2019 An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions. Applied Numerical Mathematics 139: 52–61.
  • De la Sen, M., S. Deniz, and H. Sözen, 2021 A new efficient technique for solving modified Chua’s circuit model with a new fractional operator. Advances in Difference Equations 2021: 1– 16.
  • Emin, B., and M. Yaz, 2024 Digital Implemen-tation of Chaotic Systems Using Nvidia Jetson AGX Orin andCustom DAC Converter. Chaos and Fractals 1(1): 38–41.
  • Khan A., C. Li, Z. Zhang, and X. Cen, 2025 ATwo-memristor-based Chaotic System with Symmetric Bifurcationand Multistability. Chaos and Fractals 2(1): 1–7.
  • Kiran, H. E., 2025 A Novel Chaos-Based Encryp-tion Technique with Parallel Processing Using CUDA for MobilePowerful GPU Control Center. Chaos and Fractals 1(1): 6–18.
  • Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of atmospheric sciences 20(2): 130–141.
  • Matsumoto, T., 1984 A chaotic attractor from Chua’s circuit. IEEE transactions on circuits and systems 31(12): 1055–1058.
  • Michaels, A. J., 2011 Quantitative comparisons of digital chaotic circuits for use in communications. In roceedings of the Joint INDS 11 & ISTET 11, (pp. 1–8), IEEE.
  • Peasgood, W., L. A. Dissado, C. K. Lam, A. Armstrong, and W. Wood, 2003 A novel electrical model of nerve and muscle using Pspice. Journal of Physics D: Applied Physics 36(4): 311.
  • Scherer, R., S.L. Kalla, Y. Tang, and J. Huang, 2011 The Grünwald- Letnikov method for fractional differential equations. Computers & Mathematics with Applications 62(3): 902–917.
  • Sene, N., 2021 Mathematical views of the fractional Chua’s electrical circuit described by the Caputo-Liouville derivative. Revista mexicana de fisica 67(1): 91–99.
  • Seyyarer, E., F. Ayata, and S. Özdem, 2025 The Role of Technological Approaches in Cyber Security of Au-tonomous Vehicles. ADBA Computer Science 2(1), 1–6.
  • Sheu, L. J., H.K. Chen, J. H. Chen, L. M. Tam, W. C. Chen, et al., 2008. Chaos in the Newton-–Leipnik system with fractional order. Chaos, Solitons & Fractals 36(1): 98–103.
  • Swain, S. K., D. Sain, S. K. Mishra, and S. Ghosh, 2017 Real time implementation of fractional order PID controllers for a magnetic levitation plant. AEU-International Journal of Electronics and Communications 78: 141–156.
  • Tang, K. S., K. F. Man, G. Q. Zhong, and G. Chen, 2003 Modified Chua’s circuit with x|x|. Control Theory and Application 20: 223–227.
  • Ta¸sdemir, M. F., M. Tuna, and I. Koyuncu, 2025 FPGA-Based Chaotic Oscillator Designs and Performance Analysis. Chaos and Fractals 2(1), 8–13.
  • Wang, J., L. Xiao, K. Rajagopal, A. Akgul, S. Cicek, and B. Aricioglu, 2021 Fractional-order analysis of modified Chua’s circuit system with the smooth degree of 3 and its microcontroller-based implementation with analog circuit design. Symmetry 13(2): 340.
  • Wu, C., L. Xiong, and N. Yang, 2024 Modeling and dynamics analysis of a novel fractional-order meminductive multi-stable chaotic circuit and its FPGA implementation. Chaos, Solitons & Fractals 186: 115222.
  • Wu, S., 1987 Chua’s circuit family. Proceedings of the IEEE 75(8): 1022–1032.
  • Wu, X., K. Hu, S. He, H. Wang, and Z. Zhang, 2025 A fractionalorder Chua’s system: System model, numerical simulations, hidden dynamics, DSP implementation and voice encryption application. AEU-International Journal of Electronics and Communications 155691.
  • Younis, M., H. Ahmad, M. Ozturk, and D. Singh, 2025 A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points. Alexandria Engineering Journal 110: 363–375.
  • Zou, C., X. Hu, S. Dey, L. Zhang, and X. Tang, 2017 Nonlinear fractional-order estimator with guaranteed robustness and stability for lithium-ion batteries. IEEE Transactions on Industrial Electronics 65(7): 5951–5961.

Analog Circuit Implementation of Fractional-Order Modified Chua’s Circuit

Year 2025, Volume: 7 Issue: 2, 117 - 124, 31.07.2025
https://doi.org/10.51537/chaos.1633880

Abstract

In this paper, the analog circuit implementation of a fractional-order chaotic system is presented. Fractionalization is achieved by replacing integer-order capacitors and inductors with their fractional-order counterparts in Chua’s circuit. The paper provides a model for implementing fractional-order capacitors and inductors in the circuit. The results obtained from simulating the fractional-order Chua’s circuit are compared with those derived from the Grünwald-Letnikov numerical solution. All results show strong agreement.

References

  • Abd El-Maksoud, A. J., A. A. Abd El-Kader, B. G. Hassan, M. A. Abdelhamed, N. G. Rihan, et al., 2018 FPGA implementation of fractional-order Chua’s chaotic system. In 2018 7th international conference on modern circuits and systems technologies (MOCAST), (pp. 1–4), IEEE.
  • Abd El-Maksoud, A. J., A. A. Abd El-Kader, B. G. Hassan, N. G. Rihan, M. F. Tolba, et al., 2019 FPGA implementation of sound encryption system based on fractional-order chaotic systems. Microelectronics Journal 90: 323–335.
  • Adhikary, A., S. Sen, and K. Biswas, 2016 Practical realization of tunable fractional order parallel resonator and fractional order filters. IEEE Transactions on Circuits and Systems I: Regular Papers 63(8): 1142–1151.
  • Ahmad, W., R. El-Khazali, and A. S. Elwakil, 2001 Fractional-order Wien-bridge oscillator. Electronics Letters 37(18): 1110–1112.
  • Boudjerida, N., M. S. Abdelouahab, R. Lozi, 2022 Modified projective synchronization of fractional-order hyperchaotic memristorbased Chua’s circuit. Journal of Innovative Applied Mathematics and Computational Sciences 2(3): 69–85.
  • A. Charef, H. H. Sun, Y. Y. Tsao, and B. Onaral, 1992 Fractal system as represented by singularity function. IEEE Transactions on automatic Control 37(9): 1465–1470.
  • H. Chen, F. Holland, and M. Stynes, 2019 An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions. Applied Numerical Mathematics 139: 52–61.
  • De la Sen, M., S. Deniz, and H. Sözen, 2021 A new efficient technique for solving modified Chua’s circuit model with a new fractional operator. Advances in Difference Equations 2021: 1– 16.
  • Emin, B., and M. Yaz, 2024 Digital Implemen-tation of Chaotic Systems Using Nvidia Jetson AGX Orin andCustom DAC Converter. Chaos and Fractals 1(1): 38–41.
  • Khan A., C. Li, Z. Zhang, and X. Cen, 2025 ATwo-memristor-based Chaotic System with Symmetric Bifurcationand Multistability. Chaos and Fractals 2(1): 1–7.
  • Kiran, H. E., 2025 A Novel Chaos-Based Encryp-tion Technique with Parallel Processing Using CUDA for MobilePowerful GPU Control Center. Chaos and Fractals 1(1): 6–18.
  • Lorenz, E. N., 1963 Deterministic nonperiodic flow. Journal of atmospheric sciences 20(2): 130–141.
  • Matsumoto, T., 1984 A chaotic attractor from Chua’s circuit. IEEE transactions on circuits and systems 31(12): 1055–1058.
  • Michaels, A. J., 2011 Quantitative comparisons of digital chaotic circuits for use in communications. In roceedings of the Joint INDS 11 & ISTET 11, (pp. 1–8), IEEE.
  • Peasgood, W., L. A. Dissado, C. K. Lam, A. Armstrong, and W. Wood, 2003 A novel electrical model of nerve and muscle using Pspice. Journal of Physics D: Applied Physics 36(4): 311.
  • Scherer, R., S.L. Kalla, Y. Tang, and J. Huang, 2011 The Grünwald- Letnikov method for fractional differential equations. Computers & Mathematics with Applications 62(3): 902–917.
  • Sene, N., 2021 Mathematical views of the fractional Chua’s electrical circuit described by the Caputo-Liouville derivative. Revista mexicana de fisica 67(1): 91–99.
  • Seyyarer, E., F. Ayata, and S. Özdem, 2025 The Role of Technological Approaches in Cyber Security of Au-tonomous Vehicles. ADBA Computer Science 2(1), 1–6.
  • Sheu, L. J., H.K. Chen, J. H. Chen, L. M. Tam, W. C. Chen, et al., 2008. Chaos in the Newton-–Leipnik system with fractional order. Chaos, Solitons & Fractals 36(1): 98–103.
  • Swain, S. K., D. Sain, S. K. Mishra, and S. Ghosh, 2017 Real time implementation of fractional order PID controllers for a magnetic levitation plant. AEU-International Journal of Electronics and Communications 78: 141–156.
  • Tang, K. S., K. F. Man, G. Q. Zhong, and G. Chen, 2003 Modified Chua’s circuit with x|x|. Control Theory and Application 20: 223–227.
  • Ta¸sdemir, M. F., M. Tuna, and I. Koyuncu, 2025 FPGA-Based Chaotic Oscillator Designs and Performance Analysis. Chaos and Fractals 2(1), 8–13.
  • Wang, J., L. Xiao, K. Rajagopal, A. Akgul, S. Cicek, and B. Aricioglu, 2021 Fractional-order analysis of modified Chua’s circuit system with the smooth degree of 3 and its microcontroller-based implementation with analog circuit design. Symmetry 13(2): 340.
  • Wu, C., L. Xiong, and N. Yang, 2024 Modeling and dynamics analysis of a novel fractional-order meminductive multi-stable chaotic circuit and its FPGA implementation. Chaos, Solitons & Fractals 186: 115222.
  • Wu, S., 1987 Chua’s circuit family. Proceedings of the IEEE 75(8): 1022–1032.
  • Wu, X., K. Hu, S. He, H. Wang, and Z. Zhang, 2025 A fractionalorder Chua’s system: System model, numerical simulations, hidden dynamics, DSP implementation and voice encryption application. AEU-International Journal of Electronics and Communications 155691.
  • Younis, M., H. Ahmad, M. Ozturk, and D. Singh, 2025 A novel approach to the convergence analysis of chaotic dynamics in fractional order Chua’s attractor model employing fixed points. Alexandria Engineering Journal 110: 363–375.
  • Zou, C., X. Hu, S. Dey, L. Zhang, and X. Tang, 2017 Nonlinear fractional-order estimator with guaranteed robustness and stability for lithium-ion batteries. IEEE Transactions on Industrial Electronics 65(7): 5951–5961.
There are 28 citations in total.

Details

Primary Language English
Subjects Circuits and Systems, Electrical Engineering (Other)
Journal Section Research Articles
Authors

Burak Arıcıoğlu 0000-0001-9526-7629

Publication Date July 31, 2025
Submission Date February 5, 2025
Acceptance Date April 14, 2025
Published in Issue Year 2025 Volume: 7 Issue: 2

Cite

APA Arıcıoğlu, B. (2025). Analog Circuit Implementation of Fractional-Order Modified Chua’s Circuit. Chaos Theory and Applications, 7(2), 117-124. https://doi.org/10.51537/chaos.1633880

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830 28903   

The published articles in CHTA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License Cc_by-nc_icon.svg