Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case

Many processes are mathematically simulated by systems of discrete equations with quadratic right‐hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalue λ = 1 of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.