2025/02/25 by Indranil Ghosh, Ghosh, Indranil, Hammed Olawale Fatoyinbo +1 · 1 citation
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2502.17798
openalex publication_date 2025/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We set up a system of Caputo-type fractional differential equations for a reduced-order model known as the \em denatured Morris-Lecar (dML) neurons. This neuron model has a structural similarity to a FitzHugh-Nagumo type system. We explore both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies. The main purpose of this study is to report various oscillatory phenomena (tonic spiking, mixed-mode oscillation) and bifurcations (saddle-node and Hopf) that arise with variation of the order of the fractional operator and the magnitude of the coupling strength for the coupled system. Various closed-form solutions as functions of the system parameters are established that act as the necessary and sufficient conditions for the stability of the equilibrium point. The theoretical analysis are supported by rigorous numerical simulations.