Mathematical problems of nonlinearity

Discrete-Time Dynamical Systems Generated by a Quadratic Operator

S. K. Shoyimardonov^ab, U. A. Rozikov<sup>cab

a</sup> National University of Uzbekistan, University str. 4, Tashkent, 100174 Uzbekistan
^b V. I. Romanovskiy Institute of Mathematics, University str. 9, Tashkent, 100174 Uzbekistan
^c Karshi State University, Kuchabag st. 17, Karshi, 180119 Uzbekistan

Abstract: In this paper, we examine a specific class of quadratic operators. For these operators, we identify all fixed points and categorized their types in the general case. Our analysis reveals that there are no attractive fixed points except the origin. Additionally, we investigate the global dynamics in the two-dimensional case and generalize several results obtained for lower-dimensional scenarios.

Keywords: quadratic operator, fixed point, invariant set, invariant manifold, stable curve

MSC: 34D20, 34D23, 37C25, 37C75

Received: 22.11.2024
Accepted: 12.08.2025

Language: English

DOI: 10.20537/nd250803