Dynamical Analysis and Electronic Circuit Implementation of Fractional-order Chen System

Year 2023, , 127 - 132, 31.07.2023

Abdullah Gökyıldırım

https://doi.org/10.51537/chaos.1326602

Cited By: 1

Abstract

In recent years, there has been a significant surge in interest in studies related to fractional calculus and its applications. Fractional-order analysis holds the potential to enhance the dynamic structure of chaotic systems. This study focuses on the dynamic analysis of the Chen system with low fractional-order values and its fractional-order electronic circuit. Notably, there is a lack of studies about chaotic electronic circuits in the literature with a fractional-order parameter value equal to 0.8, which makes this study pioneering in this regard. Moreover, various numerical analyses are presented to investigate the system's dynamic characteristics and complexity, such as chaotic phase planes and bifurcation diagrams. As anticipated, the voltage outputs obtained from PSpice simulations demonstrated good agreement with the numerical analysis.

Keywords

Chaos, Chen system, Fractional-order system, bifurcation, Electronic circuit implementation

References

• Ahmad, W. M. and J. C. Sprott, 2003 Chaos in fractional-order autonomous nonlinear systems. Chaos, Solitons & Fractals 16: 339–351.
• Altun, K., 2021a Fpaa implementations of fractional-order chaotic systems. Journal of Circuits, Systems and Computers 30: 2150271.
• Altun, K., 2021b Kesir dereceli sprott-k kaotik sisteminin dinamik analizi ve fpga uygulaması. Avrupa Bilim ve Teknoloji Dergisi pp. 392–399.
• Altun, K., 2022 Multi-scroll attractors with hyperchaotic behavior using fractional-order systems. Journal of Circuits, Systems and Computers 31: 2250085.
• Chen, D., C.Wu, H. H. Iu, and X. Ma, 2013 Circuit simulation for synchronization of a fractional-order and integer-order chaotic system. Nonlinear Dynamics 73: 1671–1686.
• Chen, G. and T. Ueta, 1999 Yet another chaotic attractor. International Journal of Bifurcation and chaos 9: 1465–1466.
• Dang, H. G., 2014a Adaptive synchronization of the fractionalorder sprott n system. Advanced Materials Research 850: 872– 875.
• Dang, H. G., 2014b Dynamics and synchronization of the fractionalorder sprott e system. Advanced Materials Research 850: 876– 879.
• Du, M., Z. Wang, and H. Hu, 2013 Measuring memory with the order of fractional derivative. Scientific reports 3: 3431.
• Garrappa, R., 2018 Numerical solution of fractional differential equations: A survey and a software tutorial. Mathematics 6: 16.
• Gokyildirim, A., 2023 Circuit realization of the fractional-order sprott k chaotic system with standard components. Fractal and Fractional 7: 470.
• Gokyildirim, A., H. Calgan, and M. Demirtas, 2023 Fractionalorder sliding mode control of a 4d memristive chaotic system. Journal of Vibration and Control p. 10775463231166187.
• Hosny, K. M., S. T. Kamal, and M. M. Darwish, 2022 Novel encryption for color images using fractional-order hyperchaotic system. Journal of Ambient Intelligence and Humanized Computing 13: 973–988.
• Li, C. and G. Peng, 2004 Chaos in chen’s system with a fractional order. Chaos, Solitons & Fractals 22: 443–450.
• Li, H., Y. Shen, Y. Han, J. Dong, and J. Li, 2023 Determining lyapunov exponents of fractional-order systems: A general method based on memory principle. Chaos, Solitons & Fractals 168: 113167.
• Li, X., Z. Li, and Z. Wen, 2020 One-to-four-wing hyperchaotic fractional-order system and its circuit realization. Circuit World 46: 107–115.
• Liu, T., H. Yan, S. Banerjee, and J. Mou, 2021 A fractional-order chaotic system with hidden attractor and self-excited attractor and its dsp implementation. Chaos, Solitons & Fractals 145: 110791.
• Lu, J. G. and G. Chen, 2006 A note on the fractional-order chen system. Chaos, Solitons & Fractals 27: 685–688.
• Nuñez-Perez, J.-C., V.-A. Adeyemi, Y. Sandoval-Ibarra, F.-J. Perez- Pinal, and E. Tlelo-Cuautle, 2021 Maximizing the chaotic behavior of fractional order chen system by evolutionary algorithms. Mathematics 9: 1194.
• Özkaynak, F., V. Çelik, and A. B. Özer, 2017 A new s-box construction method based on the fractional-order chaotic chen system. Signal, Image and Video Processing 11: 659–664.
• Pham, V.-T., S. T. Kingni, C. Volos, S. Jafari, and T. Kapitaniak, 2017 A simple three-dimensional fractional-order chaotic system without equilibrium: Dynamics, circuitry implementation, chaos control and synchronization. AEU-international Journal of Electronics and Communications 78: 220–227.
• Podlubny, I., 1999 Fractional differential equations, mathematics in science and engineering. Silva-Juárez, A., E. Tlelo-Cuautle, L. G. De La Fraga, and R. Li, 2020 Fpaa-based implementation of fractional-order chaotic oscillators using first-order active filter blocks. Journal of advanced research 25: 77–85.
• Sprott, J. C., 1994 Some simple chaotic flows. Physical review E 50: R647.
• Tepljakov, A. and A. Tepljakov, 2017 Fomcon: fractional-order modeling and control toolbox. Fractional-order modeling and control of dynamic systems pp. 107–129.
• Valerio, D. and J. S. Da Costa, 2004 Ninteger: a non-integer control toolbox for matlab. Proceedings of fractional differentiation and its applications, Bordeaux . Wang, B., L. Li, and Y.Wang, 2020 An efficient nonstandard finite difference scheme for chaotic fractional-order chen system. IEEE Access 8: 98410–98421.
• Wang, J., L. Xiao, K. Rajagopal, A. Akgul, S. Cicek, et al., 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: 340.
• Yang, F. and X. Wang, 2021 Dynamic characteristic of a new fractional-order chaotic system based on the hopfield neural network and its digital circuit implementation. Physica Scripta 96: 035218.
• Yao, J., K. Wang, P. Huang, L. Chen, and J. T. Machado, 2020 Analysis and implementation of fractional-order chaotic system with standard components. Journal of Advanced Research 25: 97–109.
• Zouad, F., K. Kemih, and H. Hamiche, 2019 A new secure communication scheme using fractional order delayed chaotic system: design and electronics circuit simulation. Analog Integrated Circuits and Signal Processing 99: 619–632.