IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v165y2022ip1s0960077922009286.html
   My bibliography  Save this article

Sufficient conditions and criteria for the pulse-shaped explosion related to equilibria in a class of nonlinear systems

Author

Listed:
  • Wei, Mengke
  • Han, Xiujing
  • Bi, Qinsheng

Abstract

The pulse-shaped explosion (PSE) is a novel sharp transition behavior which can give rise to bursting oscillations. Exploring a general theory applied to PSE is an important problem in the research of PSE. In this paper, we propose a two-dimensional ordinary differential equation (ODE), which can represent a class of dynamical systems with multiple-frequency slow excitations, and contribute to the theoretical understanding of the generation of PSE. Based on the fast–slow analysis, we firstly transform the ODE with multiple-frequency slow excitations into the one with a single slow variable, and thus we can obtain the fast subsystem, based on which the sufficient conditions for the existence of PSE related to equilibria are given. Then, we analyze the sufficient conditions for PSE by considering the behavior of the equilibrium theoretically. Besides, the criteria of different PSE patterns related to equilibria are developed to investigate different manifestations of PSE. Finally, the validity of the theoretical analysis is showed by numerical results of several concrete examples satisfying the class of ODE given in this paper. Our results provide the sufficient conditions and criteria for PSE involved in the proposed ODE family, and facilitate one to generate any desired dynamical systems exhibiting PSE within the framework of the suggested equation form.

Suggested Citation

  • Wei, Mengke & Han, Xiujing & Bi, Qinsheng, 2022. "Sufficient conditions and criteria for the pulse-shaped explosion related to equilibria in a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009286
    DOI: 10.1016/j.chaos.2022.112749
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922009286
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112749?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. Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Bouchnita, Anass & Jebrane, Aissam, 2020. "A hybrid multi-scale model of COVID-19 transmission dynamics to assess the potential of non-pharmaceutical interventions," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Wei, Mengke & Jiang, Wenan & Ma, Xindong & Zhang, Xiaofang & Han, Xiujing & Bi, Qinsheng, 2021. "Compound bursting dynamics in a parametrically and externally excited mechanical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Chen, Zhenyang & Chen, Fangqi, 2020. "Mixed mode oscillations induced by bi-stability and fractal basins in the FGP plate under slow parametric and resonant external excitations," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Razvan, Mohammad Reza & Yasaman, Somaye, 2020. "Emergence of bursting in two coupled neurons of different types of excitability," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Yan, Tao & Wong, Pak Kin & Ren, Hao & Wang, Huaqiao & Wang, Jiangtao & Li, Yang, 2020. "Automatic distinction between COVID-19 and common pneumonia using multi-scale convolutional neural network on chest CT scans," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    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. Wei, Mengke & Jiang, Wenan & Ma, Xindong & Zhang, Xiaofang & Han, Xiujing & Bi, Qinsheng, 2021. "Compound bursting dynamics in a parametrically and externally excited mechanical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Zhang, Shaohua & Wang, Cong & Zhang, Hongli & Ma, Ping & Li, Xinkai, 2022. "Dynamic analysis and bursting oscillation control of fractional-order permanent magnet synchronous motor system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Pasquale Cascarano & Giorgia Franchini & Erich Kobler & Federica Porta & Andrea Sebastiani, 2023. "Constrained and unconstrained deep image prior optimization models with automatic regularization," Computational Optimization and Applications, Springer, vol. 84(1), pages 125-149, January.
    4. Hanthanan Arachchilage, Kalpana & Hussaini, Mohammed Yousuff, 2021. "Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis—Effect on number of deaths," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Danjin Zhang & Youhua Qian, 2023. "Bursting Oscillations in General Coupled Systems: A Review," Mathematics, MDPI, vol. 11(7), pages 1-16, April.
    6. Qiang Wang & Min Su & Min Zhang & Rongrong Li, 2021. "Integrating Digital Technologies and Public Health to Fight Covid-19 Pandemic: Key Technologies, Applications, Challenges and Outlook of Digital Healthcare," IJERPH, MDPI, vol. 18(11), pages 1-50, June.
    7. Evgeniya V. Pankratova & Maria S. Sinitsina & Susanna Gordleeva & Victor B. Kazantsev, 2022. "Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration," Mathematics, MDPI, vol. 10(8), pages 1-20, April.
    8. Dramane Sam Idris Kanté & Aissam Jebrane & Anass Bouchnita & Abdelilah Hakim, 2023. "Estimating the Risk of Contracting COVID-19 in Different Settings Using a Multiscale Transmission Dynamics Model," Mathematics, MDPI, vol. 11(1), pages 1-19, January.
    9. Zhao, Xinxing & Li, Kainan & Ang, Candice Ke En & Cheong, Kang Hao, 2023. "A deep learning based hybrid architecture for weekly dengue incidences forecasting," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    10. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. Das, Ayan Kumar & Kalam, Sidra & Kumar, Chiranjeev & Sinha, Ditipriya, 2021. "TLCoV- An automated Covid-19 screening model using Transfer Learning from chest X-ray images," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    12. Sini V. Pillai & Ranjith S. Kumar, 2021. "The role of data-driven artificial intelligence on COVID-19 disease management in public sphere: a review," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 48(4), pages 375-389, December.
    13. Luis Vargas Tamayo & Vianney Mbazumutima & Christopher Thron & Léonard Todjihounde, 2021. "Three-Stage Numerical Solution for Optimal Control of COVID-19," Mathematics, MDPI, vol. 9(15), pages 1-26, July.
    14. Slepukhina, Evdokiia & Bashkirtseva, Irina & Ryashko, Lev & Kügler, Philipp, 2022. "Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Wei, Mengke & Han, Xiujing, 2024. "Fast–slow dynamics related to sharp transition behaviors in the Rayleigh oscillator with two slow square wave excitations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    16. Fabian Lorig & Emil Johansson & Paul Davidsson, 2021. "Agent-Based Social Simulation of the Covid-19 Pandemic: A Systematic Review," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 24(3), pages 1-5.
    17. Chang Hee Han & Misuk Kim & Jin Tae Kwak, 2021. "Semi-supervised learning for an improved diagnosis of COVID-19 in CT images," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-13, April.
    18. Cui, Hongjun & Xie, Jinping & Zhu, Minqing & Tian, Xiaoyong & Wan, Ce, 2022. "Virus transmission risk of college students in railway station during Post-COVID-19 era: Combining the social force model and the virus transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).

    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:165:y:2022:i:p1:s0960077922009286. 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.