Approximating the linear response of physical chaos
نویسندگان
چکیده
Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence chaos, rigorous computation these is certainly possible, but mathematically complicated computationally expensive. Based on Ruelle’s formalism, this paper shows that sophisticated linear response algorithm can be dramatically simplified higher-dimensional systems featuring statistical homogeneity physical space. We argue contribution SRB (Sinai–Ruelle–Bowen) measure gradient, which an integral yet most cumbersome part full algorithm, negligible if objective function appropriately aligned with unstable manifolds. This abstract condition could potentially satisfied by a vast family real-world chaotic systems, regardless meaning mathematical form perturbed parameter. demonstrate several numerical examples support conclusions present use performance algorithm. experiments, we consider models described differential equations, including Lorenz 96 Kuramoto–Sivashinsky.
منابع مشابه
on the effect of linear & non-linear texts on students comprehension and recalling
چکیده ندارد.
15 صفحه اولCONTROL OF CHAOS IN A DRIVEN NON LINEAR DYNAMICAL SYSTEM
We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...
متن کاملApproximating the Number of Linear Extensions
We approximate the number of linear extensions of an ordered set by counting “critical” suborders.
متن کاملA New Approach for Approximating Solution of Continuous Semi-Infinite Linear Programming
This paper describes a new optimization method for solving continuous semi-infinite linear problems. With regard to the dual properties, the problem is presented as a measure theoretical optimization problem, in which the existence of the solution is guaranteed. Then, on the basis of the atomic measure properties, a computation method was presented for obtaining the near optimal so...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinear Dynamics
سال: 2022
ISSN: ['1573-269X', '0924-090X']
DOI: https://doi.org/10.1007/s11071-022-07885-7