{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T21:27:48Z","timestamp":1771018068838,"version":"3.50.1"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p> Modeling and bifurcation analysis of an energy harvesting system composed of coupled resonators using the Galfenol-based magnetostrictive material are presented. The analysis in this work should be broad enough to be applicable to a large class of vibratory-based energy harvesting systems since various types of vibratory harvesters share the same normal forms, e.g. magnetostrictive and piezoelectric materials. A combined model of the mechanical and electrical domains of a single energy harvester is discussed first. Building on this model, the governing equations of the coupled system are derived, leading to a system of differential equations with an all-to-all coupling between the resonators. A bifurcation analysis of the system equations reveals different patterns of collective oscillations. Among the many different patterns, a synchronous state exists and it is stable over a broad region of parameter space. This pattern has the potential to yield significant increases in power output and it will be used as a starting point to guide future experimental work. A Hamiltonian approach is employed to study analytically the nature of the bifurcations and to calculate an expression for the onset of synchronization valid for any number of harvesters. <\/jats:p>","DOI":"10.1142\/s0218127415500261","type":"journal-article","created":{"date-parts":[[2015,2,26]],"date-time":"2015-02-26T07:18:11Z","timestamp":1424935091000},"page":"1550026","source":"Crossref","is-referenced-by-count":6,"title":["Dynamics, Bifurcations and Normal Forms in Arrays of Magnetostrictive Energy Harvesters with All-to-All Coupling"],"prefix":"10.1142","volume":"25","author":[{"given":"Antonio","family":"Matus-Vargas","sequence":"first","affiliation":[{"name":"Tecnol\u00f3gico de Monterrey, Campus Puebla, Puebla, Mexico"}]},{"given":"Hugo G.","family":"Gonz\u00e1lez-Hernandez","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico de Monterrey, Campus Puebla, Puebla, Mexico"}]},{"given":"Bernard S.","family":"Chan","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, CA 92182, USA"}]},{"given":"Antonio","family":"Palacios","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics, San Diego State University, San Diego, CA 92182, USA"}]},{"given":"Pietro-Luciano","family":"Buono","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe St N, Oshawa, ON L1H 7K4, Canada"}]},{"given":"Visarath","family":"In","sequence":"additional","affiliation":[{"name":"Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, CA 92152-5001, USA"}]},{"given":"Suketu","family":"Naik","sequence":"additional","affiliation":[{"name":"Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, CA 92152-5001, USA"}]},{"given":"Alex","family":"Phipps","sequence":"additional","affiliation":[{"name":"Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, CA 92152-5001, USA"}]},{"given":"Patrick","family":"Longhini","sequence":"additional","affiliation":[{"name":"Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, CA 92152-5001, USA"}]}],"member":"219","published-online":{"date-parts":[[2015,2,25]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4000809"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0957-0233\/17\/12\/R01"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1088\/0964-1726\/18\/9\/095029"},{"key":"rf4","volume-title":"Ordinary Differential Equations with Applications","author":"Chicone C.","year":"2000"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.080601"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413500065"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1063\/1.3159815"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.proche.2009.07.300"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/s11633-008-0334-2"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2006.1665088"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1088\/0964-1726\/16\/5\/054"},{"key":"rf14","first-page":"045102-1","volume":"68","author":"In V.","year":"2003","journal-title":"Phys. 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