IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v562y2021ics0378437120306579.html
   My bibliography  Save this article

Resonance phenomenon for a nonlinear system with fractional derivative subject to multiplicative and additive noise

Author

Listed:
  • Guo, Feng
  • Wang, Xue-yuan
  • Qin, Ming-wei
  • Luo, Xiang-dong
  • Wang, Jian-wei

Abstract

The stochastic resonance (SR) phenomenon for a nonlinear system with fractional derivative driven by multiplicative and additive noise is investigated. Applying the generalized harmonic function approach and the adiabatic elimination theory, the signal-to-noise ratio (SNR) for the system is obtained. It is found that the SNR manifests SR behavior with the variety of the system parameters, with the variety of the system characteristic frequency and that of the strength of external additive noise. The SNR behaves nonmonotonically with the system fractional exponent.

Suggested Citation

  • Guo, Feng & Wang, Xue-yuan & Qin, Ming-wei & Luo, Xiang-dong & Wang, Jian-wei, 2021. "Resonance phenomenon for a nonlinear system with fractional derivative subject to multiplicative and additive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    • Handle: RePEc:eee:phsmap:v:562:y:2021:i:c:s0378437120306579
    DOI: 10.1016/j.physa.2020.125243
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437120306579
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2020.125243?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    2. Guo, Feng & Zhu, Cheng-Yin & Cheng, Xiao-Feng & Li, Heng, 2016. "Stochastic resonance in a fractional harmonic oscillator subject to random mass and signal-modulated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 86-91.
    3. Guo, Feng & Wang, Xue-Yuan & Zhu, Cheng-Yin & Cheng, Xiao-Feng & Zhang, Zheng-Yu & Huang, Xu-Hui, 2017. "Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 205-214.
    4. Guo, Feng & Zhou, Yu-rong, 2009. "Stochastic resonance in a stochastic bistable system subject to additive white noise and dichotomous noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3371-3376.
    5. Yang, Yongge & Xu, Wei & Gu, Xudong & Sun, Yahui, 2015. "Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 190-204.
    6. Shen, Yongjun & Yang, Shaopu & Sui, Chuanyi, 2014. "Analysis on limit cycle of fractional-order van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 94-102.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Turkyilmazoglu, Mustafa & Altanji, Mohamed, 2023. "Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    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. Dai, Hongzhe & Zheng, Zhibao & Wang, Wei, 2017. "On generalized fractional vibration equation," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 48-51.
    2. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    3. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    4. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    5. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    6. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    7. Azhdari, Meysam & Binazadeh, Tahereh, 2022. "A novel adaptive SMC strategy for sustained oscillations in nonlinear sandwich systems based on stable limit cycle approach," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    8. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    9. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    10. Hakimi, A.R. & Azhdari, M. & Binazadeh, T., 2021. "Limit cycle oscillator in nonlinear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    11. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    12. Sheu, Long-Jye & Chen, Hsien-Keng & Chen, Juhn-Horng & Tam, Lap-Mou & Chen, Wen-Chin & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaos in the Newton–Leipnik system with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 98-103.
    13. Tian, Yan & Yu, Tao & He, Gui-Tian & Zhong, Lin-Feng & Stanley, H. Eugene, 2020. "The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. Li, Zengshan & Chen, Diyi & Ma, Mengmeng & Zhang, Xinguang & Wu, Yonghong, 2017. "Feigenbaum's constants in reverse bifurcation of fractional-order Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 116-123.
    15. Laskin, Nick, 2018. "Valuing options in shot noise market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 518-533.
    16. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    17. Ning, Xin & Ma, Yanyan & Li, Shuai & Zhang, Jingmin & Li, Yifei, 2018. "Response of non-linear oscillator driven by fractional derivative term under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 102-107.
    18. Trinidad Segovia, J.E. & Fernández-Martínez, M. & Sánchez-Granero, M.A., 2012. "A note on geometric method-based procedures to calculate the Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2209-2214.
    19. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.

    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:eee:phsmap:v:562:y:2021:i:c:s0378437120306579. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.