{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T10:01:35Z","timestamp":1777543295972,"version":"3.51.4"},"reference-count":43,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p> A codimension-three Takens\u2013Bogdanov bifurcation in reversible systems has been very recently analyzed in the literature. In this paper, we study with the help of the nonlinear time transformation method, the codimension-one and -two homoclinic and heteroclinic connections present in the corresponding unfolding. The algorithm developed allows to obtain high-order approximations for the global connections, in such a way that it supplies in a very efficient manner the coefficients that would be obtained with high-order Melnikov functions. As we show, all our analytical predictions have excellent agreement with the numerical results. In particular we remark that, for the two different codimension-two points, the theoretical approximation coincides in six decimal digits with the numerical continuation, even being quite far from the codimension-three point. The better approximations we provide in this work will help in the study of reversible systems that exhibit this codimension-three Takens\u2013Bogdanov bifurcation. <\/jats:p>","DOI":"10.1142\/s0218127420500170","type":"journal-article","created":{"date-parts":[[2020,2,14]],"date-time":"2020-02-14T06:35:40Z","timestamp":1581662140000},"page":"2050017","source":"Crossref","is-referenced-by-count":9,"title":["High-Order Analysis of Global Bifurcations in a Codimension-Three Takens\u2013Bogdanov Singularity in Reversible Systems"],"prefix":"10.1142","volume":"30","author":[{"given":"Bo-Wei","family":"Qin","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. 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