A map neuron with a hybrid ion channel and its dynamics

Abstract The ion channel in neurons is the basic component of signal transmission in the nervous system. The ion channel has important effects on the potential of neuron release and dynamic behavior in the neural networks. Ion channels control the flow of ions into and out of the cell membrane to form an ion current, which makes the excitable membrane produce special potential changes and become the basis of nerve and muscle activity. The blockage of ion channels has a significant effect on the dynamics of neurons and networks. Therefore, it is a very meaningful study to study the influence of ion channels on neuronal dynamics. In this work, a hybrid ion channel is designed by connecting a charge-controlled memristor (CCM) with an inductor in series, and a magnetic flux-controlled memristor (MFCM), capacitor, and nonlinear resistor are connected in parallel with the mixed ion channel to obtain the memristor neural circuit. Furthermore, the oscillator model with a hybrid ion channel and its energy function are calculated, and a map neuron is obtained by linearizing the neuron oscillator model. In addition, an adaptive regulation method is designed to explore the adaptive regulation of energy on the dynamic behaviors of the map neuron. The results show that the dynamics of a map neuron with a hybrid ion channel can be controlled by parameters and external magnetic fields. This study is also used to research on synchronization between map neurons and collective behaviors in the map neurons network.