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Algorithms 2017, 10(4), 137; doi:10.3390/a10040137

Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems

1
Centro de Desarrollo Aeroespacial, Instituto Politécnico Nacional, Ciudad de Mexico 06010, Mexico
2
Departamento de Ingeniería Agroindustrial, Universidad de Guanajuato, Campus Celaya-Salvatierra, Celaya, Guanajuato 38060, Mexico
3
Centro de Investigación en Matemáticas, Guanajuato, Guanajuato 36240, Mexico
4
Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Ciudad de México 04510, Mexico
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 19 October 2017 / Revised: 10 November 2017 / Accepted: 13 November 2017 / Published: 7 December 2017
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Abstract

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. View Full-Text
Keywords: MPI; distributed memory; Lyapunov exponents; chaos theory; non-linear dynamical systems MPI; distributed memory; Lyapunov exponents; chaos theory; non-linear dynamical systems
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Hernández-Gómez, J.J.; Couder-Castañeda, C.; Herrera-Díaz, I.E.; Flores-Guzmán, N.; Gómez-Cruz, E. Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems. Algorithms 2017, 10, 137.

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