Discrete-Time Dynamical Systems Generated by a Quadratic Operator

    Received 22 November 2024; accepted 12 August 2025; published 01 September 2025

    2025, Vol. 21, no. 3, pp.  399-418

    Author(s): Shoyimardonov S. K., Rozikov U. A.

    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 lowerdimensional scenarios.
    Keywords: quadratic operator, fixed point, invariant set, invariant manifold, stable curve
    Citation: Shoyimardonov S. K., Rozikov U. A., Discrete-Time Dynamical Systems Generated by a Quadratic Operator, Rus. J. Nonlin. Dyn., 2025, Vol. 21, no. 3, pp.  399-418
    DOI:10.20537/nd250803


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