IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v148y2021ics0960077921003970.html
   My bibliography  Save this article

Effect of time-delayed feedback in a bistable system inferred by logic operation

Author

Listed:
  • Gui, Rong
  • Li, Jiaxin
  • Yao, Yuangen
  • Cheng, Guanghui

Abstract

The effect of time delay is inferred by studying the influence of time-delayed feedback on the signal threshold of logic input signal, which reflects the width of the bistable region. Time-delayed positive feedback does not alter the width of the bistable region but increases the switching time. Time-delayed negative feedback leads to decreases in the depth of two potential wells and the width of the bistable region of the system, resulting in instability and oscillation of the system. Then, the parameter plane of the system can be divided into suprathreshold, subthreshold, oscillatory and alternate regions. With increasing time delay and negative feedback intensity, the suprathreshold and oscillatory regions continuously squeeze the middle subthreshold region until they are connected. One part of the oscillatory region is directly connected with the suprathreshold region, while the other part is transiently connected with the alternate region. There is an unstable limit cycle on the directly connected boundary. In the alternate region, the system is sensitive to initial values and system parameters and can enter two potential wells alternately with slight variations in sensitive parameters.

Suggested Citation

  • Gui, Rong & Li, Jiaxin & Yao, Yuangen & Cheng, Guanghui, 2021. "Effect of time-delayed feedback in a bistable system inferred by logic operation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003970
    DOI: 10.1016/j.chaos.2021.111043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921003970
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111043?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. Zhang, Hongxia & Xu, Wei & Guo, Qin & Han, Ping & Qiao, Yan, 2020. "First escape probability and mean first exit time for a time-delayed ecosystem driven by non-Gaussian colored noise," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Wu, Juan & Xu, Yong & Ma, Shaojuan, 2019. "Realizing the transformation of logic gates in a genetic toggle system under Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 171-179.
    3. Gui, Rong & Wang, Yue & Yao, Yuangen & Cheng, Guanghui, 2020. "Enhanced logical vibrational resonance in a two-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Shi, Peiming & Xia, Haifeng & Han, Dongying & Fu, Rongrong & Yuan, Danzhen, 2018. "Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 8-14.
    6. Nan Wang & Aiguo Song & Biao Yang, 2017. "The effect of time-delayed feedback on logical stochastic resonance," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(6), pages 1-5, June.
    7. Cheng, Guanghui & Liu, Weidan & Gui, Rong & Yao, Yuangen, 2020. "Sine-Wiener bounded noise-induced logical stochastic resonance in a two-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    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. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Cheng, Guanghui & Gui, Rong, 2022. "Bistable chaotic family and its chaotic mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Yao, Yuangen & Ma, Jun & Gui, Rong & Cheng, Guanghui, 2021. "Chaos-induced Set–Reset latch operation," Chaos, Solitons & Fractals, Elsevier, vol. 152(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. Yao, Yuangen & Ma, Jun & Gui, Rong & Cheng, Guanghui, 2021. "Chaos-induced Set–Reset latch operation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Cheng, Guanghui & Gui, Rong, 2022. "Bistable chaotic family and its chaotic mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Cheng, Guanghui & Liu, Weidan & Gui, Rong & Yao, Yuangen, 2020. "Sine-Wiener bounded noise-induced logical stochastic resonance in a two-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Gui, Rong & Wang, Yue & Yao, Yuangen & Cheng, Guanghui, 2020. "Enhanced logical vibrational resonance in a two-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Liu, Jian & Qiao, Zijian & Ding, Xiaojian & Hu, Bing & Zang, Chuanlai, 2021. "Stochastic resonance induced weak signal enhancement over controllable potential-well asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. 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).
    8. Zhang, Jingyu & Li, Xuefeng & Li, Renfu & Dai, Lu & Wang, Wei & Yang, Kai, 2021. "Internal resonance of a two-degree-of-freedom tuned bistable electromagnetic actuator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Liu, Huixia & Lu, Lulu & Zhu, Yuan & Wei, Zhouchao & Yi, Ming, 2022. "Stochastic resonance: The response to envelope modulation signal for neural networks with different topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    10. Wei, Wei & Xu, Wei & Song, Yi & Liu, Jiankang, 2021. "Bifurcation and basin stability of an SIR epidemic model with limited medical resources and switching noise," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. Liu, Jian & Cao, Jie & Wang, Youguo & Hu, Bing, 2019. "Asymmetric stochastic resonance in a bistable system driven by non-Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 321-336.
    13. Wang, Guowei & Yu, Dong & Ding, Qianming & Li, Tianyu & Jia, Ya, 2021. "Effects of electric field on multiple vibrational resonances in Hindmarsh-Rose neuronal systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    14. Hidekazu Yoshioka & Kunihiko Hamagami & Haruka Tomobe, 2023. "A Non-local Fokker-Planck Equation with Application to Probabilistic Evaluation of Sediment Replenishment Projects," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.
    15. Shi, Peiming & Xia, Haifeng & Han, Dongying & Fu, Rongrong & Yuan, Danzhen, 2018. "Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 8-14.
    16. Bi, Haohao & Lei, Youming & Han, Yanyan, 2019. "Stochastic resonance across bifurcations in an asymmetric system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1296-1312.
    17. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    18. Jiang, Jiahao & Li, Kaiyuan & Guo, Wei & Du, Luchun, 2021. "Energetic and entropic vibrational resonance," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Li, Mengdi & Shi, Peiming & Zhang, Wenyue & Han, Dongying, 2020. "Study on the optimal stochastic resonance of different bistable potential models based on output saturation characteristic and application," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    20. Wang, Xueqin & Yu, Dong & Li, Tianyu & Jia, Ya, 2023. "Logistic stochastic resonance in the Hodgkin–Huxley neuronal system under electromagnetic induction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).

    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:chsofr:v:148:y:2021:i:c:s0960077921003970. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.