{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T18:10:12Z","timestamp":1719857412669},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Hypercycles are catalytic systems with cyclic architecture. These systems have been suggested to play a key role in the maintenance and increase of information in prebiotic replicators. It is known that for a large enough number of hypercycle species ([Formula: see text]) the coexistence of all hypercycle members is governed by a stable periodic orbit. Previous research has characterized saddle-node (s-n) bifurcations involving abrupt transitions from stable hypercycles to extinction of all hypercycle members, or, alternatively, involving the outcompetition of the hypercycle by so-called mutant sequences or parasites. Recently, the presence of a bifurcation gap between a s-n bifurcation of periodic orbits and a s-n of fixed points has been described for symmetric five-member hypercycles. This gap was found between the value of the replication quality factor [Formula: see text] from which the periodic orbit vanishes ([Formula: see text]) and the value where two unstable (nonzero) equilibrium points collide ([Formula: see text]). Here, we explore the persistence of this gap considering asymmetries in replication rates in five-member hypercycles as well as considering symmetric, larger hypercycles. Our results indicate that both the asymmetry in Malthusian replication constants and the increase in hypercycle members enlarge the size of this gap. The implications of this phenomenon are discussed in the context of delayed transitions associated to the so-called saddle remnants.<\/jats:p>","DOI":"10.1142\/s021812741830001x","type":"journal-article","created":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T09:07:11Z","timestamp":1519895231000},"page":"1830001","source":"Crossref","is-referenced-by-count":1,"title":["Bifurcation Gaps in Asymmetric and High-Dimensional Hypercycles"],"prefix":"10.1142","volume":"28","author":[{"given":"J\u00falia","family":"Puig","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Av. Gregorio Mara\u00f1\u00f3n 44-50, 08028 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gerard","family":"Farr\u00e9","sequence":"additional","affiliation":[{"name":"Department of Mathematics, KTH, Royal Institute of Technology, SE-100 44 Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antoni","family":"Guillamon","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Polit\u00e8cnica de Catalunya, Av. Gregorio Mara\u00f1\u00f3n 44-50, 08028 Barcelona, Spain"},{"name":"Barcelona Graduate School of Mathematics (BGSMath), Campus de Bellaterra, Edifici C, 08193 Bellaterra, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ernest","family":"Fontich","sequence":"additional","affiliation":[{"name":"Barcelona Graduate School of Mathematics (BGSMath), Campus de Bellaterra, Edifici C, 08193 Bellaterra, Spain"},{"name":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Josep","family":"Sardany\u00e9s","sequence":"additional","affiliation":[{"name":"Barcelona Graduate School of Mathematics (BGSMath), Campus de Bellaterra, Edifici C, 08193 Bellaterra, Spain"},{"name":"Centre de Recerca Matem\u00e0tica, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,3]]},"reference":[{"key":"S021812741830001XBIB001","volume-title":"Introduction to Numerical Continuation Methods","author":"Allgower E. 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