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Spiral waves of divergence in the Barkley model of nilpotent matrices

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  • Smidtaite, Rasa
  • Ragulskis, Minvydas

Abstract

A new type of a spiral wave is presented in this paper. It is shown that spiral waves of divergence can be generated by the discrete Barkley model when all scalar nodal variables are replaced by two-dimensional nilpotent matrices of variables. However, spiral waves of divergence do not exist if scalar nodal variables of the Barkley model are replaced by idempotent matrices instead. Computational experiments demonstrate that spiral waves diverge along the centerline of the rotating bands, starting from the tip of the spiral wave – but the numerical values of the field stay bounded around zero in the regions between the rotating bands. Spiral waves of divergence are classified into five different classes according to their transient behavior. The formation of transient anti-phase clusters and Wada boundaries of five different types of spiral waves in the parameter plane of the Barkley model are examined in detail. Potential applications of spiral waves of divergence in hiding secret digital images are also discussed.

Suggested Citation

  • Smidtaite, Rasa & Ragulskis, Minvydas, 2022. "Spiral waves of divergence in the Barkley model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s096007792200368x
    DOI: 10.1016/j.chaos.2022.112158
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    References listed on IDEAS

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    1. Lu, Guangqing & Smidtaite, Rasa & Navickas, Zenonas & Ragulskis, Minvydas, 2018. "The Effect of Explosive Divergence in a Coupled Map Lattice of Matrices," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 308-313.
    2. Rajagopal, Karthikeyan & Hussain, Iqtadar & Rostami, Zahra & Li, Chunbiao & Pham, Viet-Thanh & Jafari, Sajad, 2021. "Magnetic induction can control the effect of external electrical stimuli on the spiral wave," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    3. Antonio Ambrosio & Lorenzo Marrucci & Fabio Borbone & Antonio Roviello & Pasqualino Maddalena, 2012. "Light-induced spiral mass transport in azo-polymer films under vortex-beam illumination," Nature Communications, Nature, vol. 3(1), pages 1-9, January.
    4. 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).
    5. Bukh, Andrei & Strelkova, Galina & Anishchenko, Vadim, 2019. "Spiral wave patterns in a two-dimensional lattice of nonlocally coupled maps modeling neural activity," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 75-82.
    6. Lu, Guangqing & Smidtaite, Rasa & Howard, Daniel & Ragulskis, Minvydas, 2019. "An image hiding scheme in a 2-dimensional coupled map lattice of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 78-85.
    7. López Garza, Gabriel & Nicolás Mata, Aurelio & Román Alonso, Graciela & Godínez Fernández, José Rafael & Castro García, Miguel Alfonso, 2022. "Cell-to-cell mathematical modeling of arrhythmia phenomena in the heart," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 153-172.
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    Cited by:

    1. Zeng, Ziyue & Xiao, Fuyuan, 2023. "A new complex belief entropy of χ2 divergence with its application in cardiac interbeat interval time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Smidtaite, Rasa & Ragulskis, Minvydas, 2024. "Finite-time divergence in Chialvo hyperneuron model of nilpotent matrices," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

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