Abstract
A delay-differential equationɛu(t)+u(t)=f(u(t−1)), 0⩽t < ∞, and its generalization are investigated in the limitɛ → 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent ofɛ. As for the attractor, it can be regarded as a direct product ofO(1/ɛ) equivalent “subattractors,” their statistical characteristics being asymptotically independent of ɛ. The results enable one to predict some characteristics of the attractor with fractal dimensionD ≫ 1 for the caseɛ ≪ 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.
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Ershov, S.V. Asymptotic theory of multidimensional chaos. J Stat Phys 69, 781–812 (1992). https://doi.org/10.1007/BF01050434
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DOI: https://doi.org/10.1007/BF01050434