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Cognitive Neurodynamics

, Volume 13, Issue 4, pp 393–407 | Cite as

Bifurcation analysis and diverse firing activities of a modified excitable neuron model

  • Argha Mondal
  • Ranjit Kumar UpadhyayEmail author
  • Jun Ma
  • Binesh Kumar Yadav
  • Sanjeev Kumar Sharma
  • Arnab Mondal
Research Article

Abstract

Electrical activities of excitable cells produce diverse spiking-bursting patterns. The dynamics of the neuronal responses can be changed due to the variations of ionic concentrations between outside and inside the cell membrane. We investigate such type of spiking-bursting patterns under the effect of an electromagnetic induction on an excitable neuron model. The effect of electromagnetic induction across the membrane potential can be considered to analyze the collective behavior for signal processing. The paper addresses the issue of the electromagnetic flow on a modified Hindmarsh–Rose model (H–R) which preserves biophysical neurocomputational properties of a class of neuron models. The different types of firing activities such as square wave bursting, chattering, fast spiking, periodic spiking, mixed-mode oscillations etc. can be observed using different injected current stimulus. The improved version of the model includes more parameter sets and the multiple electrical activities are exhibited in different parameter regimes. We perform the bifurcation analysis analytically and numerically with respect to the key parameters which reveals the properties of the fast-slow system for neuronal responses. The firing activities can be suppressed/enhanced using the different external stimulus current and by allowing a noise induced current. To study the electrical activities of neural computation, the improved neuron model is suitable for further investigation.

Keywords

Improved H–R model Electromagnetic induction effect Bifurcation Various neuronal responses Noise 

Notes

Acknowledgements

This work is supported by the Council of Scientific and Industrial Research (CSIR), Govt. of India under Grant No. 25(0277)/17/EMR-II) to the author (R. K. Upadhyay).

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia
  2. 2.Computational Neuroscience CenterUniversity of WashingtonSeattleUSA
  3. 3.Department of PhysicsLanzhou University of TechnologyLanzhouPeople’s Republic of China

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