Comparative analysis of Runge-Kutta, ODE45, and Euler Methods with Bifurcation Analysis for Modeling Pottasium and Calcium Channel Dynamics in the Morris-Lecar Neuron Model. Netriani Veminsyah Ahda
Bengkulu University
Abstract
The analysis of neuronal excitability and signal transmission can be approached quantitatively through the utilization of simulations of membrane potential dynamics, utilizing biophysical models. The present study investigates axonal membrane potential behavior based on the Morris-Lecar model, which describes neuronal activity in terms of interactions between potassium and calcium ions. A series of numerical simulations was conducted in the programming language MATLAB, utilizing the Euler, Runge-Kutta and ODE45 methods to solve the nonlinear differential equations that govern the membrane potential and ion channel variables. The bifurcation analysis method was utilized to identify critical transitions in neuronal states, including shifts from resting to spiking or bursting activity. This provides insight into the mechanisms underlying normal and pathological neuronal behavior. A comparative analysis reveals that the Runge-Kutta and ODE45 methods demonstrate enhanced accuracy and stability in comparison to the Euler method. Notably, the ODE45 method exhibits adaptive time-step efficiency. These findings underscore the most efficacious numerical approach for modeling ion transport and neuronal dynamics, thereby contributing to a more comprehensive understanding of neurophysiological processes and the mechanisms underlying neurological disorders.
Keywords: Transport Ion, Morris-Lecar Neuron Model, Numerical Methods, Bifurcation
