Universal quantification for deterministic chaos in dynamical systems

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dc.creatorSelvam, A. Mary
dc.date2000-08-04
dc.date.accessioned2026-07-07T05:44:22Z
dc.date.available2026-07-07T05:44:22Z
dc.descriptionA cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model predicts the following: (a) The phase space trajectory (strange attractor) when resolved as a function of the computer accuracy has intrinsic logarithmic spiral curvature with the quasiperiodic Penrose tiling pattern for the internal structure. (b) The universal constant for deterministic chaos is identified as the steady-state fractional round-off error k for each computational step and is equal to 1 /sqr(tau) (=0.382) where tau is the golden mean. (c) The Feigenbaum's universal constants a and d are functions of k and, further, the expression 2(a**2) = (pie)*d quantifies the steady-state ordered emergence of the fractal geometry of the strange attractor. (d) The power spectra of chaotic dynamical systems follow the universal and unique inverse power law form of the statistical normal distribution.
dc.description8 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/physics/0008010
dc.identifierhttp://arxiv.org/abs/physics/0008010
dc.identifierApplied Mathematical Modelling, 1993, Vol.17, 642-649
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/83617
dc.subjectGeneral Physics
dc.titleUniversal quantification for deterministic chaos in dynamical systems
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