Stability of nonlinear autonomous quadratic discrete systems in the critical case (Q1958772)

Summary: 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 \(\lambda =1\) of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.