{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T12:43:11Z","timestamp":1771072991070,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,11]]},"abstract":"<jats:p> This paper is concerned with how the symmetry and singularity of a system of differential equations affect generic dynamics and bifurcations. By computation of Hopf-pitchfork point in a two-parameter nonlinear problem satisfying a [Formula: see text]-symmetry condition, the mode interactions in two-parameter bifurcations with a single zero and two pairs of imaginary roots are considered. The codimension two normal form with equivariant Hopf-pitchfork bifurcations are given. Through analyzing the unfolding structure, local classification in the neighborhood of equivariant Hopf-pitchfork bifurcations point for the [Formula: see text]-symmetric is undertaken. A rich variety of dynamical and bifurcation behaviors is pointed out. Beyond a stable fixed point or a pair of stable fixed points, some interesting phenomena are also found, such as the coexistence of two periodic solutions which are verified both theoretically and numerically. <\/jats:p>","DOI":"10.1142\/s0218127416502059","type":"journal-article","created":{"date-parts":[[2016,11,22]],"date-time":"2016-11-22T07:46:26Z","timestamp":1479800786000},"page":"1650205","source":"Crossref","is-referenced-by-count":4,"title":["Equivariant Hopf-Pitchfork Bifurcation of Symmetric Coupled Neural Network with Delay"],"prefix":"10.1142","volume":"26","author":[{"given":"Baodong","family":"Zheng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Harbin Institute of Technology, Harbin 150040, P. 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