IEEE Trans Neural Netw Learn Syst. 2020 Feb;31(2):502-511. doi: 10.1109/TNNLS.2019.2905137. Epub 2019 Apr 11.
Memristors can be employed to mimic biological neural synapses or to describe electromagnetic induction effects. To exhibit the threshold effect of electromagnetic induction, this paper presents a threshold flux-controlled memristor and examines its frequency-dependent pinched hysteresis loops. Using an electromagnetic induction current generated by the threshold memristor to replace the external current in 2-D Hindmarsh-Rose (HR) neuron model, a 3-D memristive HR (mHR) neuron model with global hidden oscillations is established and the corresponding numerical simulations are performed. It is found that due to no equilibrium point, the obtained mHR neuron model always operates in hidden bursting firing patterns, including coexisting hidden bursting firing patterns with bistability also. In addition, the model exhibits complex dynamics of the actual neuron electrical activities, which acts like the 3-D HR neuron model, indicating its feasibility. In particular, by constructing the fold and Hopf bifurcation sets of the fast-scale subsystem, the bifurcation mechanisms of hidden bursting firings are expounded. Finally, circuit experiments on hardware breadboards are deployed and the captured results well match with the numerical results, validating the physical mechanism of biological neuron and the reliability of electronic neuron.
忆阻器可用于模拟生物神经网络突触或描述电磁感应效应。为了表现出电磁感应的阈值效应，本文提出了一种具有阈值磁通控制的忆阻器，并研究了其频率相关的磁滞回线。利用阈值忆阻器产生的电磁感应电流代替二维 Hindmarsh-Rose（HR）神经元模型中的外部电流，建立了具有全局隐藏振荡的三维忆阻 HR（mHR）神经元模型，并进行了相应的数值模拟。结果发现，由于不存在平衡点，所得到的 mHR 神经元模型总是处于隐藏爆发点火模式下工作，包括具有双稳性的共存隐藏爆发点火模式。此外，该模型表现出了实际神经元电活动的复杂动力学，其行为类似于三维 HR 神经元模型，表明其具有可行性。特别是，通过构造快尺度子系统的折叠和 Hopf 分岔集，阐述了隐藏爆发点火的分岔机制。最后，在硬件面包板上进行了电路实验，所捕获的结果与数值结果吻合较好，验证了生物神经元的物理机制和电子神经元的可靠性。
