Modulational instability in chain diffusive neuronal networks under electric field

In this paper, the impact of electric field on the emergence and propagation of nonlinear wave impulse is investigated through modulational instability in an improved chain FitzHugh-Nagumo neuronal network. Through the application of the powerful multiple scale expansion method on the system of N-differential equations, we obtain the angular frequency of modulated impulse wave along the network. This frequency is showed to be dependent on the electric field feedback gain as well as the coupling strength of the network. Our analytical predictions agree with the numerical results. The formation of localized nonlinear wave patterns is confirmed. The spatiotemporal pattern for action potential shows that electric feedback gain and high-frequency field modulate the wave patterns by promoting the emergence of chaotic-like wave patterns while high-intensity external electric field is showed to suppress wave patterns completely. The sampled time series revealed the high-intensity external field suppresses the electrical activities, by reducing the output to quiescent state. Extensive numerical simulations revealed the network supports burst synchronization, recurrent in the manifestation of paroxysmal epilepsy.

Automated summary

This paper investigates the impact of electric field on the emergence and propagation of a nonlinear wave impulse in an improved neuronal network. The angular frequency of the modulated impulse wave along the network is obtained through the application of the multiple scale expansion method. The frequency is found to be dependent on the electric field feedback gain and the coupling strength of the network. The results confirm the formation of localized nonlinear wave patterns and show that electric feedback gain and high-frequency field promote the emergence of chaotic-like wave patterns, while high-intensity external electric field suppresses wave patterns completely. The sampled time series analysis reveals that high-intensity external field suppresses electrical activities by reducing the output to a quiescent state. Extensive numerical simulations also demonstrate burst synchronization in the network, recurrently manifesting as paroxysmal epilepsy.