Cognitive Neurodynamics

, Volume 12, Issue 2, pp 235–254 | Cite as

Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction

  • Zahra Rostami
  • Sajad Jafari
Research Article


Complex anatomical and physiological structure of an excitable tissue (e.g., cardiac tissue) in the body can represent different electrical activities through normal or abnormal behavior. Abnormalities of the excitable tissue coming from different biological reasons can lead to formation of some defects. Such defects can cause some successive waves that may end up to some additional reorganizing beating behaviors like spiral waves or target waves. In this study, formation of defects and the resulting emitted waves in an excitable tissue are investigated. We have considered a square array network of neurons with nearest-neighbor connections to describe the excitable tissue. Fundamentally, electrophysiological properties of ion currents in the body are responsible for exhibition of electrical spatiotemporal patterns. More precisely, fluctuation of accumulated ions inside and outside of cell causes variable electrical and magnetic field. Considering undeniable mutual effects of electrical field and magnetic field, we have proposed the new Hindmarsh–Rose (HR) neuronal model for the local dynamics of each individual neuron in the network. In this new neuronal model, the influence of magnetic flow on membrane potential is defined. This improved model holds more bifurcation parameters. Moreover, the dynamical behavior of the tissue is investigated in different states of quiescent, spiking, bursting and even chaotic state. The resulting spatiotemporal patterns are represented and the time series of some sampled neurons are displayed, as well.


Neuronal network Pattern formation Spiral wave Magnetic flow Electromagnetic induction 



Sajad Jafari was supported by Iran National Science Foundation (No. 96000815). The authors would like to thank Dr. Fatemeh Hadaeghi for help and comments which enhanced the quality of this paper.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Biomedical Engineering DepartmentAmirkabir University of TechnologyTehranIran

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