Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems
نویسندگان
چکیده
Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge–Kutta problems that need to be calculated. In this work we introduce a parallel implementation based on MPI (Message Passing Interface) for the calculation of the Lyapunov exponents for a multidimensional dynamical system, considering a weakly coupled algorithm. Since we work on an academic high-latency cluster interconnected with a gigabit switch, the design has to be oriented to reduce the number of messages required. With the design introduced in this work, the computing time is drastically reduced, and the obtained performance leads to close to optimal speed-up ratios. The implemented parallelisation allows us to carry out many experiments for the calculation of several Lyapunov exponents with a low-cost cluster. The numerical experiments showed a high scalability, which we showed with up to 68 cores.
منابع مشابه
Computations of the Lyapunov exponents from time series
In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefo...
متن کاملLyapunov Exponents of Free Operators
Lyapunov exponents of a dynamical system are a useful tool to gauge the stability and complexity of the system. This paper offers a definition of Lyapunov exponents for a sequence of free linear operators. The definition is based on the concept of the extended Fuglede-Kadison determinant. We establish the existence of Lyapunov exponents, derive formulas for their calculation, and show that Lyap...
متن کاملLyapunov Exponents for Non-classical Multidimensional Continued Fraction Algorithms
We introduce a simple geometrical two-dimensional continued fraction algorithm inspired from dynamical renormalization. We prove that the algorithm is weakly convergent, and that the associated transformation admits an ergodic absolutely continuous invariant probability measure. Following Lagarias, its Lyapunov exponents are related to the approximation exponents which measure the diophantine q...
متن کاملInvariant Pre-foliations for Non-resonant Non-uniformly Hyperbolic Systems
Given an orbit whose linearization has invariant subspaces satisfying some non-resonance conditions in the exponential rates of growth, we prove existence of invariant manifolds tangent to these subspaces. The exponential rates of growth can be understood either in the sense of Lyapunov exponents or in the sense of exponential dichotomies. These manifolds can correspond to “slow manifolds”, whi...
متن کاملA Semi-invertible Oseledets Theorem with Applications to Transfer Operator Cocycles
Oseledets’ celebrated Multiplicative Ergodic Theorem (MET) [V.I. Oseledec, A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179–210.] is concerned with the exponential growth rates of vectors under the action of a linear cocycle on Rd. When the linear actions are invertible, the MET guarantees an almost-everywhere poi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Algorithms
دوره 10 شماره
صفحات -
تاریخ انتشار 2017