A controlled Murali-Lakshmanan-Chua memristor circuit to mimic neuron dynamics

This paper deals with the problem of modelling the classical dynamics of cortical neurons by using memristor circuits. A simple model, based on a controlled Murali-Lakshmanan-Chua memristor circuit, is proposed. The control law exploits the foliation property of circuits with ideal memristors in the uncontrolled case, which is at the basis of their dynamical richness, together with a mechanism able to mimic the typical neuron responses, such as regular and fast spiking, intrinsic bursting and chattering. To facilitate the electronic implementation of the circuit, the control input employs a sequence of sawtooth impulsive signals for the feedforward term and comparators and hysteresis blocks for the feedback terms. It is also shown that the designed control law is robust with respect the possible lack of ideality of memristors, due, e.g., to imperfections in their practical realization.