Unstable discrete modes in Hindmarsh–Rose neural networks under magnetic flow effect

The competitive effect between electric and magnetic flux couplings is used, in the context of modulational instability, to describe the collective dynamics in a modified Hindmarsh–Rose neural networks. The multiple-scale expansion is utilized to reduce the system to a nonlinear differential-difference equation, whose plane wave solutions are found to be unstable for some values of parameters. Particular interest is given to the influence of changing both the electric and magnetic coupling strengths, and confirmation of analytical results is given via numerical integration of the generic Hindmarsh–Rose model. The model presents a rich variety of spatiotemporal patterns propagating in the network, as the result of the interplay between nonlinear and dispersive effects. The electromagnetic induction appears to be responsible for regular bursting patterns and synchronous states in the network. With increasing the electric coupling, full synchronization is difficult to realize and irregular spatiotemporal patterns of action potentials are predominant.