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Cognitive Neurodynamics
Published in: Cognitive Neurodynamics 2/2021

23-06-2020 | Research Article

Complex bifurcation analysis and synchronization optimal control for Hindmarsh–Rose neuron model under magnetic flow effect

Authors: Marcel Kemayou Wouapi, Bertrand Hilaire Fotsin, Elie Bertrand Megam Ngouonkadi, Florent Feudjio Kemwoue, Zeric Tabekoueng Njitacke

Published in: Cognitive Neurodynamics | Issue 2/2021

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Abstract

In this contribution, the complex behaviour of the Hindmarsh–Rose neuron model under magnetic flow effect (mHR) is investigated in terms of bifurcation diagrams, Lyapunov exponent plots and time series when varying only the electromagnetic induction strength. Some exciting phenomena are found including, for instance, various firings patterns by applying appropriate magnetic strength and Hopf-fold bursting through fast–slow bifurcation. In addition to this, the interesting phenomenon of Hopf bifurcation is examined in the model. Thus, we prove that Hopf bifurcation occurs in this memristor-based HR neuron model when an appropriately chosen magnetic flux varies and reaches its critical value. Furthermore, one of the main results of this work was the optimal control approach to realize the synchronization of two mHR. The main advantage of the proposed optimal master–slave synchronization from a control point of view is that, in the practical application, the electrical activities (quiescent, bursting, spiking, period and chaos states) of a neuron can be regulated by a pacemaker (master) associated with biological neuron (slave) to treat some diseases such as epilepsy. A suitable electronic circuit is designed and used for the investigations. PSpice based simulation results confirm that the electrical activities and synchronization between coupled neurons can be modulated by electromagnetic flux.
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Appendix
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Metadata
Title
Complex bifurcation analysis and synchronization optimal control for Hindmarsh–Rose neuron model under magnetic flow effect
Authors
Marcel Kemayou Wouapi
Bertrand Hilaire Fotsin
Elie Bertrand Megam Ngouonkadi
Florent Feudjio Kemwoue
Zeric Tabekoueng Njitacke
Publication date
23-06-2020
Publisher
Springer Netherlands
Published in
Cognitive Neurodynamics / Issue 2/2021
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-020-09606-5

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