{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:16:41Z","timestamp":1760242601669,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,12,7]],"date-time":"2017-12-07T00:00:00Z","timestamp":1512604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007161","name":"Secretar\u00eda de Investigaci\u00f3n y Posgrado, Instituto Polit\u00e9cnico Nacional","doi-asserted-by":"publisher","award":["20171536","20170721","20171027"],"award-info":[{"award-number":["20171536","20170721","20171027"]}],"id":[{"id":"10.13039\/501100007161","id-type":"DOI","asserted-by":"publisher"}]},{"name":"CDA\/IPN","award":["FS0001"],"award-info":[{"award-number":["FS0001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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\u2013Kutta 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.<\/jats:p>","DOI":"10.3390\/a10040137","type":"journal-article","created":{"date-parts":[[2017,12,7]],"date-time":"2017-12-07T11:49:10Z","timestamp":1512647350000},"page":"137","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Weakly Coupled Distributed Calculation of Lyapunov Exponents for Non-Linear Dynamical Systems"],"prefix":"10.3390","volume":"10","author":[{"given":"Jorge","family":"Hern\u00e1ndez-G\u00f3mez","sequence":"first","affiliation":[{"name":"Centro de Desarrollo Aeroespacial, Instituto Polit\u00e9cnico Nacional, Ciudad de Mexico 06010, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8826-3750","authenticated-orcid":false,"given":"Carlos","family":"Couder-Casta\u00f1eda","sequence":"additional","affiliation":[{"name":"Centro de Desarrollo Aeroespacial, Instituto Polit\u00e9cnico Nacional, Ciudad de Mexico 06010, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2117-7548","authenticated-orcid":false,"given":"Israel","family":"Herrera-D\u00edaz","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Agroindustrial, Universidad de Guanajuato, Campus Celaya-Salvatierra, Celaya, Guanajuato 38060, Mexico"}]},{"given":"Norberto","family":"Flores-Guzm\u00e1n","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Matem\u00e1ticas, Guanajuato, Guanajuato 36240, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3090-0395","authenticated-orcid":false,"given":"Enrique","family":"G\u00f3mez-Cruz","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Ciudad Universitaria, Ciudad de M\u00e9xico 04510, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,7]]},"reference":[{"key":"ref_1","unstructured":"Strogatz, S. 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