Exploring the Complex Neuronal Excitabilities in a Fractional-Order Generalized FHN System
Year: 2026
Type: article
Abstract: In this work, a generalized FitzHugh-Nagumo (FHN) biophysical model is presented under fractional-order Caputo formalism. We incorporate a memory-dependent response function and diverse neuronal excitatory-oscillatory characteristics that yield fractional-order dynamics (FOD) with previous history-dependent properties in the excitable system. We focus our study on a particular example of the FHN model with a sigmoidal recovery term that produces the alternation of spiking-bursting phenomena, including mixed-mode oscillations. The symmetric bursting behavior is observed with an appropriate recovery variable. This system exhibits dynamical features that are qualitatively comparable to those observed in cortical cell activities, particularly regarding the transition between excitatory states in neuronal dynamics. In the fractional-order domain, we show that the system produces such transitions in the firing statistics as the fractional exponent is decreased from the integer order. Then, we examine the variations in firing characteristics using the stability analysis and bifurcation in a suitable parameter space. The system replicates fascinating dynamics that can be more resistant to switching on various high-level activities by increasing the memory response function. We show that the generalized fractional-order FHN model captures memory-trace-dependent dynamics; numerical simulations validate the analysis.
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,645
OpenAlex ID: W7225636010