Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case - Josef Diblík; Denys Ya. Khusainov; Irina V. Grytsay; Zdenĕk Šmarda (Discrete Dynamics in Nature and Society)
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.