{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T04:40:37Z","timestamp":1777610437785,"version":"3.51.4"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"14","funder":[{"name":"NSF-Chia","award":["11290141"],"award-info":[{"award-number":["11290141"]}]},{"name":"NSF-Chia","award":["11371047"],"award-info":[{"award-number":["11371047"]}]},{"name":"NSF-Chia","award":["11422111"],"award-info":[{"award-number":["11422111"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,12,30]]},"abstract":"<jats:p> The decay of a planar compact surface that is reduced through its boundary is considered. The interest of this problem lies in the fact that it can represent the destruction of a solid tumor by a population of immune cells. The theory of curves is utilized to derive the rate at which the area of the set decreases. Firstly, the process is represented as a discrete dynamical system. A recurrence equation describing the shrinkage of the area at any step is deduced. Then, a continuum limit is attained to derive an ordinary differential equation that governs the decay of the set. The solutions to the differential equation and its implications are discussed, and numerical simulations are carried out to test the accuracy of the decay law. Finally, the dynamics of a tumor-immune aggregate is inspected using this law and the theory of bifurcations. As the ratio of immune destruction to tumor growth increases, a saddle-node bifurcation stabilizes the tumor-free fixed point. <\/jats:p>","DOI":"10.1142\/s0218127417502236","type":"journal-article","created":{"date-parts":[[2018,1,28]],"date-time":"2018-01-28T22:58:05Z","timestamp":1517180285000},"page":"1750223","source":"Crossref","is-referenced-by-count":11,"title":["Bifurcation Analysis and Nonlinear Decay of a Tumor in the Presence of an Immune Response"],"prefix":"10.1142","volume":"27","author":[{"given":"\u00c1lvaro G.","family":"L\u00f3pez","sequence":"first","affiliation":[{"name":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s\/n, 28933 M\u00f3stoles, Madrid, Spain"}]},{"given":"Jes\u00fas M.","family":"Seoane","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s\/n, 28933 M\u00f3stoles, Madrid, Spain"}]},{"given":"Miguel A. F.","family":"Sanju\u00e1n","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de F\u00edsica, Universidad Rey Juan Carlos, Tulip\u00e1n s\/n, 28933 M\u00f3stoles, Madrid, Spain"},{"name":"Department of Applied Informatics, Kaunas University of Technology, Studentu 50-415, Kaunas LT-51368, Lithuania"},{"name":"Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA"}]}],"member":"219","published-online":{"date-parts":[[2018,1,28]]},"reference":[{"key":"S0218127417502236BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(00)00143-6"},{"key":"S0218127417502236BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(03)00133-X"},{"key":"S0218127417502236BIB003","doi-asserted-by":"publisher","DOI":"10.1158\/0008-5472.CAN-05-0564"},{"key":"S0218127417502236BIB004","first-page":"5475","volume":"56","author":"Gatenby R. 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