Bifurcation analysis and network investigation of a Fitzhugh–Nagumo-based neuron model with combined effects of the external current and electrical field

Analysis of a dynamic system helps scientists understand its properties and utilize it properly in different applications. This study analyzes the effects of various external excitements on a recently proposed mathematical neuron model derived from the original Fitzhugh–Nagumo model. Different bifurcation analyses on this system are conducted to detect chaotic behaviors that are common and of great importance in biological systems, considering the effects of different types of external excitements. Lyapunov exponents (LEs) confirm the existence of chaotic patterns. Furthermore, a bifurcation diagram that looks into the changes in the system dynamics caused by the simultaneous application of the external stimulants is represented. Neurons are bound to play a role in a network in which synchrony is an analytical quality. Therefore, the potential of a network of this model in showing synchronization is examined using the master stability function (MSF) technique. Ultimately, it is concluded that this neural model can produce chaotic behaviors and synchronous networks.