Asymptotic theory of multidimensional chaos |
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Authors: | Sergey V Ershov |
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Institution: | (1) Keldysh Institute for Applied Mathematics, 125047 Moscow, Russia |
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Abstract: | A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems. |
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Keywords: | Chaos delay-differential equation domain structure invariant distribution |
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