Dynamical Behaviors for a Discrete Two-Neuron System

In this paper, a discrete two-neuron system is investigated, wherein the comparison principle, invariant sets, existence, non-existence, and stability of steady-state solutions are established. These results are new, sharp, and valid for high-dimensional systems. Numerical simulations not only confirmed the obtained theoretical results but also inspired some new reflections. Furthermore, a new local stability theorem and its corollary are derived by applying the Courant-Weyl inequalities. In particular, the obtained theoretical results and numerical simulations will be beneficial for more general bistable discrete systems.