Elimination of spiral waves in excitable media by magnetic induction

Elimination of spiral waves in excitable media by magnetic induction The formation of spiral waves in excitable media is a fascinating example of the beauty of nonlinear dynamics in spatiotemporal systems. Apart from the beauty of the patterns, the subject also has many practical application. For example, the emergence of spiral waves in cardiac tissue can lead to arrhythmias. Cortical spiral waves are also involved in epileptic seizures. Motivated by this, we here study the effects of magnetic induction on the formation of spiral waves in excitable media. An external sinusoidal magnetic induction with different amplitudes and angular frequencies is applied in order to study whether spiral waves could be eliminated. We use a network of coupled neurons as a model for the excitable medium. The four-variable magnetic Hindmarsh–Rose model is used for the local dynamics of each isolated neuron. The distribution of the cell membrane potential over time, affected by magnetic induction, is determined and the results are depicted as snapshots of the 2D network. Our research reveals that the continuance of rotating spiral seeds is impaired by high-amplitude magnetic induction. Moreover, we show that low-frequency induction is not capable of breaking the reorganizing rhythm of the spiral seeds, while much higher frequencies can be too fast to overcome this special rhythm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Elimination of spiral waves in excitable media by magnetic induction

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
DOI
10.1007/s11071-018-4385-9
Publisher site
See Article on Publisher Site

Abstract

The formation of spiral waves in excitable media is a fascinating example of the beauty of nonlinear dynamics in spatiotemporal systems. Apart from the beauty of the patterns, the subject also has many practical application. For example, the emergence of spiral waves in cardiac tissue can lead to arrhythmias. Cortical spiral waves are also involved in epileptic seizures. Motivated by this, we here study the effects of magnetic induction on the formation of spiral waves in excitable media. An external sinusoidal magnetic induction with different amplitudes and angular frequencies is applied in order to study whether spiral waves could be eliminated. We use a network of coupled neurons as a model for the excitable medium. The four-variable magnetic Hindmarsh–Rose model is used for the local dynamics of each isolated neuron. The distribution of the cell membrane potential over time, affected by magnetic induction, is determined and the results are depicted as snapshots of the 2D network. Our research reveals that the continuance of rotating spiral seeds is impaired by high-amplitude magnetic induction. Moreover, we show that low-frequency induction is not capable of breaking the reorganizing rhythm of the spiral seeds, while much higher frequencies can be too fast to overcome this special rhythm.

Journal

Nonlinear Dynamics – Springer Journals

Published: Jun 1, 2018

References

  • Simple lessons from complexity
    Goldenfeld, N; Kadanoff, LP
  • Simplicity and complexity in the description of nature
    Gell-Mann, M
  • Stability of subsystem solutions in agent-based models
    Perc, M
  • Complex systems: physics beyond physics
    Holovatch, Y; Kenna, R; Thurner, S
  • Collective response, synapse coupling and field coupling in neuronal network
    Guo, S; Xu, Y; Wang, C; Jin, W; Hobiny, A; Ma, J
  • Multi-channels coupling-induced pattern transition in a tri-layer neuronal network
    Wu, F; Wang, Y; Ma, J; Jin, W; Hobiny, A
  • Autapse-induced multiple coherence resonance in single neurons and neuronal networks
    Yilmaz, E; Ozer, M; Baysal, V; Perc, M
  • Non-fragile synchronization control for markovian jumping complex dynamical networks with probabilistic time-varying coupling delays
    Li, X; Rakkiyappan, R; Sakthivel, N
  • Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations
    Li, X; Fu, X
  • A review for dynamics in neuron and neuronal network
    Ma, J; Tang, J
  • Network science of biological systems at different scales: a review
    Gosak, M; Markovič, R; Dolenšek, J; Rupnik, MS; Marhl, M; Stožer, A; Perc, M
  • Loosening the shackles of scientific disciplines with network science: reply to comments on network science of biological systems at different scales: a review
    Gosak, M; Markovič, R; Dolenšek, J; Rupnik, MS; Marhl, M; Stožer, A; Perc, M
  • Epilepsy as a Dynamic Disease
    Milton, J; Jung, P
  • Collective responses in electrical activities of neurons under field coupling
    Xu, Y; Jia, Y; Ma, J; Hayat, T; Alsaedi, A
  • A review and guidance for pattern selection in spatiotemporal system
    Wang, C; Ma, J
  • Pattern formation in diffusive excitable systems under magnetic flow effects
    Mvogo, A; Takembo, CN; Fouda, HPE; Kofané, TC
  • Modulated wave formation in myocardial cells under electromagnetic radiation
    Takembo, CN; Mvogo, A; Ekobena Fouda, HP; Kofané, TC
  • Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties
    Xiang, W; Huangpu, Y
  • Patterns in Excitable Media: Genesis, Dynamics, and Control
    Sinha, S; Sridhar, S
  • The dynamics of spiral tip adjacent to inhomogeneity in cardiac tissue
    Zhang, J; Tang, J; Ma, J; Luo, JM; Yang, XQ
  • Approximated spiral and target patterns in Bazykins prey-predator model: Multiscale perturbation analysis
    Banerjee, M; Ghorai, S; Mukherjee, N
  • Spiral waves in a coupled network of sine-circle maps
    Woo, S-J; Lee, J; Lee, KJ
  • Selection of multiarmed spiral waves in a regular network of neurons
    Hu, B; Ma, J; Tang, J
  • Pattern selection in network of coupled multi-scroll attractors
    Li, F; Ma, J
  • Effects of small-world connectivity on noise-induced temporal and spatial order in neural media
    Perc, M
  • Elimination of spiral waves in cardiac tissue by multiple electrical shocks
    Panfilov, AV; Müller, SC; Zykov, VS; Keener, JP
  • Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle
    Pertsov, AM; Davidenko, JM; Salomonsz, R; Baxter, WT; Jalife, J
  • Visualization of spiral and scroll waves in simulated and experimental cardiac tissue
    Cherry, EM; Fenton, FH
  • Introduction: mapping and control of complex cardiac arrhythmias
    Christini, DJ; Glass, L
  • Spatial and temporal organization during cardiac fibrillation
    Gray, RA; Pertsov, AM; Jalife, J
  • Flow detection of propagating waves with temporospatial correlation of activity
    Takagaki, K; Zhang, C; Wu, J-Y; Ohl, FW
  • Dynamical evolution of spatiotemporal patterns in mammalian middle cortex
    Schiff, SJ; Huang, X; Wu, J-Y
  • Elimination of spiral waves in a locally connected chaotic neural network by a dynamic phase space constraint
    Li, Y; Oku, M; He, G; Aihara, K
  • Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation
    Ge, M; Jia, Y; Xu, Y; Yang, L
  • Suppression of firing activities in neuron and neurons of network induced by electromagnetic radiation
    Li, J; Liu, S; Liu, W; Yu, Y; Wu, Y
  • Model of electrical activity in cardiac tissue under electromagnetic induction
    Wu, F; Wang, C; Xu, Y; Ma, J
  • Multiple modes of electrical activities in a new neuron model under electromagnetic radiation
    Lv, M; Ma, J
  • Phase synchronization between two neurons induced by coupling of electromagnetic field
    Ma, J; Mi, L; Zhou, P; Xu, Y; Hayat, T
  • Transcranial magnetic stimulation-coil design with improved focality
    Rastogi, P; Lee, E; Hadimani, RL; Jiles, DC
  • A model of the nerve impulse using two first-order differential equations
    Hindmarsh, J; Rose, R
  • A quantitative description of membrane current and its application to conduction and excitation in nerve
    Hodgkin, AL; Huxley, AF
  • Lévy noise improves the electrical activity in a neuron under electromagnetic radiation
    Wu, J; Xu, Y; Ma, J
  • Model of electrical activity in a neuron under magnetic flow effect
    Lv, M; Wang, C; Ren, G; Ma, J; Song, X
  • Memristor-the missing circuit element
    Chua, L
  • Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays
    Li, X; Rakkiyappan, R; Velmurugan, G
  • The missing memristor found
    Strukov, DB; Snider, GS; Stewart, DR; Williams, RS
  • Synchronization of identical and nonidentical memristor-based chaotic systems via active backstepping control technique
    Rakkiyappan, R; Sivasamy, R; Li, X
  • Principles of Neural Science
    Kandel, ER; Schwartz, JH; Jessell, TM; Siegelbaum, SA; Hudspeth, AJ
  • Properties of action-potential initiation in neocortical pyramidal cells: evidence from whole cell axon recordings
    Shu, Y; Duque, A; Yu, Y; Haider, B; McCormick, DA

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