In this paper, we investigate the wave propagation phenomenon and network dynamics of an improved Hindmarsh–Rose neuron model considered with magnetic induction. The dynamical properties of the improved neuron model in discussed with the help of eigenvalues, Lyapunov exponents and bifurcation plots. A simple comparison between the exponential flux model and quadratic flux model is investigated and shown that the exponential flux model could show behavior like the quadratic model with its memductance monotonically increasing or decreasing depending on the polarity of the voltage. In the network dynamics investigation, we have considered two additional external disturbances such as the noise and flux excitation. A mathematical model of a lattice array with Box–Mueller type random noise and a sinusoidal periodic flux excitation is defined. The wave propagation phenomenon in the presence of noise is investigated using the noise variance as the control parameter. We could show that when the noise is applied to the network for the entire simulation time, the spiral waves are effectively suppressed for very low noise variance values.