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Investigates the upper semi-continuity of numerical attractors in lattice systems, suggesting stability in dynamics as step size decreases.
This paper investigates the dynamics of lattice systems with fractional Laplacian. We first establish the existence of global attractors for the lattice systems and numerical attractors for the implicit Euler scheme. Subsequently, we rigorously prove the upper semi-continuity of these numerical attractors as the discretization step size approaches zero.
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Li et al. (2026) studied this question.
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