Modeling and behavioral analysis of neurons under direction-dependent resistive, inductive and capacitive coupling

Abstract

This study exploits the modeling and behavioral analysis of electrical coupling medium between neurons. A new electrical coupling model that represents two resistor, inductor and capacitor (RLC) circuits for a single link between two neurons is introduced by employing the biological evidences and electrical circuit theory knowledge. Herein, a model consisting of a network of multiple FitzHugh–Nagumo (FHN) neurons in a ring topology is also proposed. The presented model follows direction-dependent transmission based on resistive, inductive, and capacitive inter-neuronal electrical coupling medium for generalization purposes. The coupling medium, attributable to the direction-dependent information transmittance, admitting resistive, inductive and capacitive nature, reveals the astonished results such as the existence of two PID controllers for a single link among two neurons. Furthermore, the effects of difference in PID parameters by fixing the parametric difference and by increasing the parametric difference on synchronization are studied in order to explore the behavior of electrical coupling medium. Astoundingly, such behavioral analysis reveals that the coupling medium truly tracks the well-known proportional integral derivative (PID) characteristics curve.