Open AccessComplex bifurcation analysis and synchronization optimal control for Hindmarsh–Rose neuron model under magnetic flow effect
Author(s) -
Marcel Kemayou Wouapi,
B. Hilaire Fotsin,
Elie Bertrand Megam Ngouonkadi,
Florent Feudjio Kemwoue,
Zeric Tabekoueng Njitacke
Publication year - 2020
Publication title -
cognitive neurodynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.83
H-Index - 41
eISSN - 1871-4099
pISSN - 1871-4080
DOI - 10.1007/s11571-020-09606-5
Subject(s) - biological neuron model , bursting , lyapunov exponent , hopf bifurcation , bifurcation , synchronization (alternating current) , control theory (sociology) , computer science , bifurcation diagram , physics , mathematics , statistical physics , chaotic , artificial neural network , topology (electrical circuits) , artificial intelligence , control (management) , neuroscience , quantum mechanics , nonlinear system , combinatorics , biology
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.