IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v178y2024ics0960077923012195.html
   My bibliography  Save this article

Spiral waves in fractal dimensions and their elimination in λ − ω systems with less damaging intervention

Author

Listed:
  • El-Nabulsi, Rami Ahmad
  • Anukool, Waranont

Abstract

The theory of spiral waves in excitable media is considered an important topic in several dynamical systems. They have been observed in various physicochemical and biological systems such as the Belousov-Zhabotinsky chemical reactions, lethal arrhythmia in the heart, amoebas Dictyostelium discoideium, disinhibited mammalian neocortex retinal spreading depression, and seizures in the brain. In this study, spiral waves in an excitable system are analytically studied in fractal dimensions based on the theory of integration and differentiation for a non-integer dimensional space. We consider the generic oscillatory model λ−ω system characterized by a rotational symmetry where spiral waves are expected to occur. It was observed that for lower fractal dimensions with respect to unity, spiral waves may be suppressed in an excitable media without destroying the propagation of normal waves. This may be considered as an alternative approach to experimental and numerical approaches found in the literature. Their eliminations are important since they forbid the transition to a chaotic state in excitable media. Our approach could contribute to an improved therapy of clinical conditions such as atrial fibrillation and suppressing arrhythmias in cardiac models.

Suggested Citation

  • El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2024. "Spiral waves in fractal dimensions and their elimination in λ − ω systems with less damaging intervention," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
  • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012195
    DOI: 10.1016/j.chaos.2023.114317
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923012195
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.114317?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. Olmos-Liceaga, Daniel & Ocejo-Monge, Humberto, 2017. "On the generation of spiral and scroll waves by periodic stimulation of excitable media in the presence of obstacles of minimum size," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 162-170.
    2. Rajagopal, Karthikeyan & Wei, Zhouchao & Moroz, Irene & Karthikeyan, Anitha & Duraisamy, Prakash, 2020. "Elimination of spiral waves in a one-layer and two-layer network of pancreatic beta cells using a periodic stimuli," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Yuan, Guoyong & Liu, Pengwei & Shi, Jifang & Wang, Guangrui, 2023. "Dynamics and control of spiral waves under feedback derived from a moving measuring point," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Hu, Yipeng & Ding, Qianming & Wu, Yong & Jia, Ya, 2023. "Polarized electric field-induced drift of spiral waves in discontinuous cardiac media," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    5. Karthikeyan Rajagopal & Shirin Panahi & Mo Chen & Sajad Jafari & Bocheng Bao, 2021. "Suppressing Spiral Wave Turbulence In A Simple Fractional-Order Discrete Neuron Map Using Impulse Triggering," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-10, December.
    6. Ma, Jun & Wang, Chun-Ni & Li, Yan-Long & Li, Shi-Rong, 2007. "Suppression of spiral waves in light-sensitive media using chaotic signal modulated scheme," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 965-970.
    7. Rajagopal, Karthikeyan & Karthikeyan, Anitha, 2022. "Spiral waves and their characterization through spatioperiod and spatioenergy under distinct excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    8. Xu, Binbin & Jacquir, Sabir & Laurent, Gabriel & Bilbault, Jean-Marie & Binczak, Stéphane, 2011. "A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 633-639.
    9. Rajagopal, Karthikeyan & Jafari, Sajad & Li, Chunbiao & Karthikeyan, Anitha & Duraisamy, Prakash, 2021. "Suppressing spiral waves in a lattice array of coupled neurons using delayed asymmetric synapse coupling," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Parastesh, Fatemeh & Rajagopal, Karthikeyan & Alsaadi, Fawaz E. & Hayat, Tasawar & Pham, V.-T. & Hussain, Iqtadar, 2019. "Birth and death of spiral waves in a network of Hindmarsh–Rose neurons with exponential magnetic flux and excitable media," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 377-384.
    11. Etémé, A.S. & Tabi, C.B. & Mohamadou, A. & Kofané, T.C., 2019. "Elimination of spiral waves in a two-dimensional Hindmarsh–Rose neural network under long-range interaction effect and frequency excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    12. Ding, Qianming & Wu, Yong & Hu, Yipeng & Liu, Chaoyue & Hu, Xueyan & Jia, Ya, 2023. "Tracing the elimination of reentry spiral waves in defibrillation: Temperature effects," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    13. Balamurali Ramakrishnan & Ramesh Ramamoorthy & Chunbiao Li & Akif Akgul & Karthikeyan Rajagopal, 2021. "Spiral Waves in a Lattice Array of Josephson Junction Chaotic Oscillators with Flux Effects," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, January.
    14. Ma, Jun & Jia, Ya & Yi, Ming & Tang, Jun & Xia, Ya-Feng, 2009. "Suppression of spiral wave and turbulence by using amplitude restriction of variable in a local square area," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1331-1339.
    15. Wang, Zhen & Rostami, Zahra & Jafari, Sajad & Alsaadi, Fawaz E. & Slavinec, Mitja & Perc, Matjaž, 2019. "Suppression of spiral wave turbulence by means of periodic plane waves in two-layer excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 229-233.
    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. Hu, Yipeng & Ding, Qianming & Wu, Yong & Jia, Ya, 2023. "Polarized electric field-induced drift of spiral waves in discontinuous cardiac media," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Nezhad Hajian, Dorsa & Parastesh, Fatemeh & Jafari, Sajad & Perc, Matjaž & Klemenčič, Eva, 2024. "Medium inhomogeneities modulate emerging spiral waves," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Rajagopal, Karthikeyan & Nezhad Hajian, Dorsa & Natiq, Hayder & Peng, Yuexi & Parastesh, Fatemeh & Jafari, Sajad, 2024. "Effect of Gaussian gradient in the medium's action potential morphology on spiral waves," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    4. 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).
    5. Li, Fan & Liu, Shuai & Li, Xiaola, 2022. "Pattern selection in thermosensitive neuron network induced by noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    6. Yuan, Guoyong & Liu, Pengwei & Shi, Jifang & Wang, Guangrui, 2023. "Dynamics and control of spiral waves under feedback derived from a moving measuring point," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    7. Yuan, Guoyong & Xu, Lin & Xu, Aiguo & Wang, Guangrui & Yang, Shiping, 2011. "Spiral waves in excitable media due to noise and periodic forcing," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 728-738.
    8. Luo, Hao-jie & Xue, Yu & Huang, Mu-yang & Zhang, Qiang & Zhang, Kun, 2024. "Pattern and waves on 2D-Kuramoto model with many-body interactions," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    9. Zhou, Ping & Ma, Jun & Xu, Ying, 2023. "Phase synchronization between neurons under nonlinear coupling via hybrid synapse," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    10. Rajagopal, Karthikeyan & Jafari, Sajad & Li, Chunbiao & Karthikeyan, Anitha & Duraisamy, Prakash, 2021. "Suppressing spiral waves in a lattice array of coupled neurons using delayed asymmetric synapse coupling," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    11. Puebla, Hector & Martin, Roland & Alvarez-Ramirez, Jose & Aguilar-Lopez, Ricardo, 2009. "Controlling nonlinear waves in excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 971-980.
    12. Ding, Qianming & Wu, Yong & Hu, Yipeng & Liu, Chaoyue & Hu, Xueyan & Jia, Ya, 2023. "Tracing the elimination of reentry spiral waves in defibrillation: Temperature effects," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    13. Balamurali Ramakrishnan & Victor Kamdoum Tamba & Hayder Natiq & Alex Stephane Kemnang Tsafack & Anitha Karthikeyan, 2022. "Dynamical analysis of autonomous Josephson junction jerk oscillator with cosine interference term embedded in FPGA and investigation of its collective behavior in a network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-12, September.
    14. Smidtaite, Rasa & Ragulskis, Minvydas, 2022. "Spiral waves of divergence in the Barkley model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    15. Rostami, Zahra & Pham, Viet-Thanh & Jafari, Sajad & Hadaeghi, Fatemeh & Ma, Jun, 2018. "Taking control of initiated propagating wave in a neuronal network using magnetic radiation," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 141-151.
    16. Rajagopal, Karthikeyan & Karthikeyan, Anitha, 2022. "Spiral waves and their characterization through spatioperiod and spatioenergy under distinct excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    17. Rajgopal, Karthikeyan & Karthikeyan, Anitha & V.R., Varun Raj, 2022. "Dynamical behavior of pancreatic β cells with memductance flux coupling: Considering nodal properties and wave propagation in the excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    18. Li, Fan, 2020. "Effect of field coupling on the wave propagation in the neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    19. Rostami, Zahra & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Jafari, Sajad & Perc, Matjaž & Slavinec, Mitja, 2018. "Wavefront-obstacle interactions and the initiation of reentry in excitable media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1162-1173.
    20. Ma, Jun & Xu, Ying & Wang, Chunni & Jin, Wuyin, 2016. "Pattern selection and self-organization induced by random boundary initial values in a neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 586-594.

    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:178:y:2024:i:c:s0960077923012195. 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.