{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:22:24Z","timestamp":1763389344444,"version":"3.37.3"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["VICI 639.033.008"],"award-info":[{"award-number":["VICI 639.033.008"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NWO Cluster Nonlinear Dynamics in Natural Systems"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,6,15]]},"abstract":"<jats:p> Tip growth is a growth stage which occurs in fungal cells. During tip growth, the cell exhibits continuous extreme lengthwise growth while its shape remains qualitatively the same. A model for single celled fungal tip growth is given by the Ballistic Aging Thin viscous Sheet (BATS) model, which consists of a five-dimensional system of first-order differential equations. The solutions of the BATS model that correspond to fungal tip growth arise through a codimension-1 global bifurcation in a two-parameter family of solutions. In this paper we derive a toy model from the BATS model. The toy model is given by two-dimensional system of first-order differential equations which depend on a single parameter. The main achievement of this paper is a proof that the toy model exhibits an analogue of the codimension-1 global bifurcation in the BATS model. An important ingredient of the proof is a topological method which enables the identification of the bifurcation points. Finally, we discuss how the proof may be generalized to the BATS model. <\/jats:p>","DOI":"10.1142\/s0218127420501072","type":"journal-article","created":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T09:25:33Z","timestamp":1593595533000},"page":"2050107","source":"Crossref","is-referenced-by-count":4,"title":["Fungal Tip Growth Arising Through a Codimension-1 Global Bifurcation"],"prefix":"10.1142","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8295-6898","authenticated-orcid":false,"given":"T. G.","family":"de Jong","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. E.","family":"Sterk","sequence":"additional","affiliation":[{"name":"Bernoulli Institute, University of Groningen, P. O. Box 407, 9700 AK Groningen, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. 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