IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4678394.html
   My bibliography  Save this article

Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model

Author

Listed:
  • Changjin Xu
  • Peiluan Li
  • Maoxin Liao
  • Zixin Liu
  • Qimei Xiao
  • Shuai Yuan

Abstract

In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.

Suggested Citation

  • Changjin Xu & Peiluan Li & Maoxin Liao & Zixin Liu & Qimei Xiao & Shuai Yuan, 2019. "Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model," Complexity, Hindawi, vol. 2019, pages 1-15, September.
    • Handle: RePEc:hin:complx:4678394
    DOI: 10.1155/2019/4678394
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4678394.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/4678394.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/4678394?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2019. "Difference synchronization among three chaotic systems with exponential term and its chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 36-51.
    2. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    3. Yang, Jihua & Zhao, Liqin, 2015. "Bifurcation analysis and chaos control of the modified Chua’s circuit system," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 332-339.
    4. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    5. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sangpet, Teerawat & Kuntanapreeda, Suwat, 2020. "Finite-time synchronization of hyperchaotic systems based on feedback passivation," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Fu, Shihui & Liu, Yuan & Ma, Huizhen & Du, Ying, 2020. "Control chaos to different stable states for a piecewise linear circuit system by a simple linear control," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Usama, B.I. & Morfu, S. & Marquie, P., 2021. "Vibrational resonance and ghost-vibrational resonance occurrence in Chua’s circuit models with specific nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Jie Zhang & Jiliang Lv & Nana Cheng & Xiaodong Wei & Liu Yang, 2025. "Mismatch synchronization based on 4D memristive chaotic system and its application in image encryption," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(4), pages 1-21, April.
    5. García, P., 2022. "A machine learning based control of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    7. Xuan, Deli & Tang, Ze & Feng, Jianwen & Park, Ju H., 2021. "Cluster synchronization of nonlinearly coupled Lur’e networks: Delayed impulsive adaptive control protocols," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    10. Fang, Guochang & Tian, Lixin & Fu, Min & Sun, Mei & Du, Ruijin & Liu, Menghe, 2017. "Investigating carbon tax pilot in YRD urban agglomerations—Analysis of a novel ESER system with carbon tax constraints and its application," Applied Energy, Elsevier, vol. 194(C), pages 635-647.
    11. Hao, Zhang & Xing-yuan, Wang & Peng-fei, Yan & Yu-jie, Sun, 2020. "Combination synchronization and stability analysis of time-varying complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    12. Ziye Zhang & Xiaoping Liu & Chong Lin & Bing Chen, 2018. "Finite-Time Synchronization for Complex-Valued Recurrent Neural Networks with Time Delays," Complexity, Hindawi, vol. 2018, pages 1-14, December.
    13. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2021. "Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 562-580.
    14. Tang, Xiaosong, 2022. "Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 420-429.
    15. Yang, Te & Chen, Guoliang & Xia, Jianwei & Wang, Zhen & Sun, Qun, 2019. "Robust H∞ filtering for polytopic uncertain stochastic systems under quantized sampled outputs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 688-701.
    16. Kai, Yue & Chen, Shuangqing & Zheng, Bailin & Zhang, Kai & Yang, Nan & Xu, Wenlong, 2020. "Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    17. Prants, Fabiola G. & Rech, Paulo C., 2017. "Complex dynamics of a three-dimensional continuous-time autonomous system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 132-139.
    18. Tiwari, Ankit & Singh, Piyush Pratap & Roy, Binoy Krishna, 2024. "A realizable chaotic system with interesting sets of equilibria, characteristics, and its underactuated predefined-time sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    19. Wang, Yang & Li, Huanyun & Guan, Yan & Chen, Mingshu, 2022. "Predefined-time chaos synchronization of memristor chaotic systems by using simplified control inputs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. Anand, Pallov & Sharma, Bharat Bhushan, 2020. "Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:4678394. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.