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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,12,15]]},"abstract":"<jats:p> In this paper, we investigate the complex dynamics of a mapping derived from a differential equation with simple time-periodic delay. Firstly, we calculate the truncated normal form of 1:1 resonance of the mapping at a degenerate fixed point and obtain an approximating system of the mapping by using Picard iteration. By analyzing the approximate system, we find that the mapping will undergo a 1:1 resonance at the degenerate fixed point. Secondly, the qualitative property and the stability of the degenerate fixed point are determined, which provide a new view to understand the dynamic of differential equation with simple time-periodic delay. However, the approximate system does not have the versal unfolding of the Bogdanov\u2013Takens singularity of codimension 2. These phenomena show that simple time-periodic delay can support complex dynamics. Finally, a numerical simulation is carried out to verify the analytic results. <\/jats:p>","DOI":"10.1142\/s0218127423501754","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T06:08:11Z","timestamp":1702361291000},"source":"Crossref","is-referenced-by-count":0,"title":["Simple Time-Periodic Delay Can Support Complex Dynamics"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4067-1760","authenticated-orcid":false,"given":"Mingshan","family":"Li","sequence":"first","affiliation":[{"name":"College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, P. R. China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7368-1746","authenticated-orcid":false,"given":"Naiming","family":"Xie","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211106, P. R. 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