DYNAMICAL BEHAVIORS FOR A DISCRETE TWO-NEURON SYSTEM
Abstract
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.
Fields of Study & Subjects
Neural Networks Stability and Synchronization
Advanced Differential Equations and Dynamical Systems
Mathematical and Theoretical Epidemiology and Ecology Models
Publication details
- Journal / source
- Journal of Applied Analysis & Computation
- Volume
- 16
- Issue
- 4
- Pages
- 1843–1859
- Publication date
- 1 January 2026
- Language
- EN