Analysis reveals no attractive fixed points in quadratic operator dynamics, suggesting stability concerns in two-dimensional systems.
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.
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Shoyimardonov et al. (2025) studied this question.
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