{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:34:44Z","timestamp":1762353284692,"version":"3.41.2"},"reference-count":42,"publisher":"World Scientific Pub Co Pte Ltd","issue":"12","funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["FRF-IDRY-19-027"],"award-info":[{"award-number":["FRF-IDRY-19-027"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,9,30]]},"abstract":"<jats:p> In this research, we offer a bifurcation analysis to describe impacting, stick, and grazing between a particle and the piston to better understand the nonlinear dynamics of a Fermi oscillator. The principles of hybrid dynamical systems will be utilized to explain the moving process in such a Fermi oscillator. The motion complexity and stick mechanism of such an oscillator are demonstrated using periodic and chaotic motions. We introduce the hybrid dynamical system and numerical continuation detection tool COCO. Physical and mathematical models are used to construct the obtained bounded mathematical model. The frequency, amplitude in oscillating base displacement, and the gap between the stationary boundary and the piston\u2019s equilibrium position are the major parameters. We employ path-following analysis to illustrate the bifurcation that leads to solution destabilization. From the viewpoint of eigenvalue analysis, the essence of period-doubling and Fold bifurcation is revealed. Numerical continuation methods are used to perform a complete one-parameter bifurcation analysis of the Fermi oscillator. The presence of codimension-1 bifurcations of limit cycles, like period-doubling, fold, and grazing bifurcations, is shown in this work. Then, the one-parameter continuation analysis is tracked in two-parameter bifurcation diagrams that include a second important factor of interest. Bifurcations cause all solutions to lose stability, according to our findings. The acquired results provide a better understanding of the Fermi oscillator mechanism and demonstrate that we may control the system dynamics by modifying the parameters. <\/jats:p>","DOI":"10.1142\/s0218127422501796","type":"journal-article","created":{"date-parts":[[2022,10,13]],"date-time":"2022-10-13T08:12:06Z","timestamp":1665648726000},"source":"Crossref","is-referenced-by-count":2,"title":["Bifurcation and Path-Following Analysis of Periodic Orbits of a Fermi Oscillator Model"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6176-9911","authenticated-orcid":false,"given":"Wei","family":"Ma","sequence":"first","affiliation":[{"name":"School of Civil and Resource Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, P. R. China"}]},{"given":"Tafara","family":"Mapuranga","sequence":"additional","affiliation":[{"name":"School of Civil and Resource Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing 100083, P. R. China"}]},{"given":"Jiguang","family":"Zhang","sequence":"additional","affiliation":[{"name":"XCMG Construction Machinery Co. Ltd., Dahuangshan Road, Gulou District, Xuzhou, Jiangsu 221004, P. R. China"}]},{"given":"Hejiang","family":"Ding","sequence":"additional","affiliation":[{"name":"XCMG Construction Machinery Co. Ltd., Dahuangshan Road, Gulou District, Xuzhou, Jiangsu 221004, P. R. China"}]},{"given":"Jiandong","family":"Chen","sequence":"additional","affiliation":[{"name":"Tangshan Jidong Equipment and Engineering Co., Ltd., Qiancao Road, Caofeidian District, Tangshan, Heibei 063200, P. R. China"}]},{"given":"Xiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Tangshan Jidong Equipment and Engineering Co., Ltd., Qiancao Road, Caofeidian District, Tangshan, Heibei 063200, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"key":"S0218127422501796BIB001","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.5154"},{"key":"S0218127422501796BIB002","doi-asserted-by":"publisher","DOI":"10.5890\/JAND.2015.11.003"},{"key":"S0218127422501796BIB003","first-page":"299","volume":"8","author":"Bazhenov V.","year":"2019","journal-title":"Discont. Nonlin. 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