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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2024,3,30]]},"abstract":"<jats:p> In this paper, we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts from a cooperator to a degrader. At the bifurcation caused by this functional shift, an invariant curve collapses to a point [Formula: see text] while, simultaneously, two fixed points collide with [Formula: see text] in a transcritical bifurcation. Moreover, all points of a line containing [Formula: see text] become fixed points at the bifurcation and only at the bifurcation in a degenerate scenario. We provide a complete analytical description of this degenerate bifurcation. As a result of our study, we prove the existence of the invariant curve arising from the transition to cooperation. <\/jats:p>","DOI":"10.1142\/s0218127424500457","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T07:56:00Z","timestamp":1711007760000},"source":"Crossref","is-referenced-by-count":1,"title":["Functional Shift-Induced Degenerate Transcritical Neimark\u2013Sacker Bifurcation in a Discrete Hypercycle"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2415-9310","authenticated-orcid":false,"given":"Ernest","family":"Fontich","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona (UB), Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain"},{"name":"Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8268-4503","authenticated-orcid":false,"given":"Antoni","family":"Guillamon","sequence":"additional","affiliation":[{"name":"Centre de Recerca Matem\u00e0tica (CRM), Cerdanyola del Vall\u00e8s, 08193 Barcelona, Catalonia, Spain"},{"name":"Departament de Matem\u00e0tiques and IMTech, Universitat Polit\u00e8cnica de Catalunya, EPSEB, Av. 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