A Discrete Saccadic Model and Bursting

Abstract

One of the eye movements is the saccade, which has led to the introduction of the saccadic model. This study is based on the part of the saccadic model, which means the burst neurons and resettable integrator model. The principal limitation of the original model is the lack of differentiability at the equilibrium point. By using the Naka–Rushton function, we introduce a new model in place of the original one, so that the equilibrium point of the system becomes a differentiable point in the modified model. Our focus in this work is to investigate the fundamental properties of the discrete model of our novel system. We apply the forward Euler method to transform the new model to a discrete model. With the utilization of the center manifold theory, we describe some of its dynamical features, such as stability, instability, and bifurcation at a fixed point. Finally, both analytical and numerical simulations are used to continue investigating the period-doubling bifurcation according to the numerical parameters in the saccadic model.