A Simplified Hindmarsh-Rose Model Based on Power-Flow Analysis

The Hindmarsh-Rose model is known as a neuron model that can display various neuronal dynamics such as spiking and bursting. Circuit implementations are mostly based on operational amplifiers and transistors, while a theoretical, equivalent electrical circuit of this widely used model has only been recently proposed. This circuit provides a good tool for analyzing the importance of the individual circuit elements with respect to the overall behavior, but contains several highly nonlinear circuit elements. For this reason, we propose a simplified, equivalent circuit by investigating the power flows of the nonlinear circuit elements. As a result, we obtain a circuit where a resistor remains as the only nonlinear circuit element. Simulation results verify the circuit's ability to still generate spiking and bursting dynamics. Moreover, a bifurcation analysis reveals that there exist clearly separable spiking and bursting regimes. This allows for a well controllable behavior of the simplified circuit.