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January 18, 2026Open Access

On a Global Attractor for a Class of One-Dimensional Autonomous Systems

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Mathematical analysis establishes stability and existence of equilibria in one-dimensional systems, suggesting broader applications.

The study aims to analyze the stability and existence of equilibria in one-dimensional autonomous differential equations.
Investigated one-dimensional autonomous ordinary differential equations on a bounded interval.
Examined equilibria and stability conditions under minimal regularity and monotonicity assumptions.
Analyzed the impact of the dimensionless parameter κ on the attractor location.
Establish existence of equilibria and uniqueness of a stable equilibrium on the increasing branch of H(x).
Demonstrated global asymptotic stability within the invariant interval for the stable equilibrium.
Proved structural stability of the attractor under small parameter perturbations.

Aleksander Kubanski (2026) studied this question.

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