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.

在此贡献中，当仅改变电磁感应强度时，根据分岔图、李雅普诺夫指数图和时间序列研究了 Hindmarsh-Rose 神经元模型在磁流效应 (mHR) 下的复杂行为。发现了一些令人兴奋的现象，例如，通过应用适当的磁场强度和通过快-慢分叉的 Hopf 折叠爆发的各种发射模式。除此之外，模型中还检查了有趣的 Hopf 分岔现象。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. 此外，这项工作的主要成果之一是实现两个 mHR 同步的最佳控制方法。从控制的角度来看，所提出的最佳主从同步的主要优点是，在实际应用中，神经元的电活动（静止、突发、尖峰、周期和混沌状态）可以由起搏器调节（主）与生物神经元（从）相关联，治疗癫痫等一些疾病。设计了一个合适的电子电路并将其用于研究。基于 PSpice 的模拟结果证实，耦合神经元之间的电活动和同步可以通过电磁通量进行调制。神经元的周期和混沌状态）可以通过与生物神经元（从）相关的起搏器（主）来调节，以治疗癫痫等疾病。设计了一个合适的电子电路并将其用于研究。基于 PSpice 的模拟结果证实，耦合神经元之间的电活动和同步可以通过电磁通量进行调制。神经元的周期和混沌状态）可以通过与生物神经元（从）相关的起搏器（主）来调节，以治疗癫痫等疾病。设计了一个合适的电子电路并将其用于研究。基于 PSpice 的模拟结果证实，耦合神经元之间的电活动和同步可以通过电磁通量进行调制。