{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:56:42Z","timestamp":1760237802460,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,8,12]],"date-time":"2022-08-12T00:00:00Z","timestamp":1660262400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Agency","award":["ANR-18-EURE-0016-528"],"award-info":[{"award-number":["ANR-18-EURE-0016-528"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Nonlinear dynamics have become a new perspective on model human movement variability; however, it is still a debate whether chaotic behavior is indeed possible to present during a rhythmic movement. This paper reports on the nonlinear dynamical behavior of coupled and synchronization models of a planar rhythmic arm movement. Two coupling schemes between a planar arm and an extended Duffing-Van der Pol (DVP) oscillator are investigated. Chaos tools, namely phase space, Poincare section, Lyapunov Exponent (LE), and heuristic approach are applied to observe the dynamical behavior of orbit solutions. For the synchronization, an orientation angle is modeled as a single well DVP oscillator implementing a Proportional Derivative (PD)-scheme. The extended DVP oscillator is used as a drive system, while the orientation angle of the planar arm is a response system. The results show that the coupled system exhibits very rich dynamical behavior where a variety of solutions from periodic, quasi-periodic, to chaotic orbits exist. An advanced coupling scheme is necessary to yield the route to chaos. By modeling the orientation angle as the single well DVP oscillator, which can synchronize with other dynamical systems, the synchronization can be achieved through the PD-scheme approach.<\/jats:p>","DOI":"10.3390\/bioengineering9080385","type":"journal-article","created":{"date-parts":[[2022,8,14]],"date-time":"2022-08-14T21:09:06Z","timestamp":1660511346000},"page":"385","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coupled and Synchronization Models of Rhythmic Arm Movement in Planar Plane"],"prefix":"10.3390","volume":"9","author":[{"given":"Affiani","family":"Machmudah","sequence":"first","affiliation":[{"name":"Faculty of Advanced Technology and Multidiscipline, Kampus C Jalan Mulyorejo, Universitas Airlangga, Surabaya 60115, Indonesia"},{"name":"Research Center for Hydrodynamics Technology, National Research and Innovation Agency (BRIN), Jl. Hidro Dinamika, Keputih, Sukolilo, Surabaya 60112, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5247-2788","authenticated-orcid":false,"given":"Denys","family":"Dutykh","sequence":"additional","affiliation":[{"name":"Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, 73000 Chamb\u00e9ry, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Setyamartana","family":"Parman","sequence":"additional","affiliation":[{"name":"Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Durian Tunggal, Melaka 76100, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1038\/35065745","article-title":"Synchronization and rhythmic processes in physiology","volume":"410","author":"Glass","year":"2001","journal-title":"Nature"},{"key":"ref_2","unstructured":"Bernstein, N.A. (1967). 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