OSCILLATIONS IN A CAMP SIGNALING MODEL FOR CELL AGGREGATION { A GEOMETRIC ANALYSIS

Zhouqian Miao, Nikola Popovic, Peter Szmolyan

Research output: Contribution to journalArticlepeer-review

Abstract

We study a singularly perturbed model for a cyclic adenosine monophosphate(cAMP) signaling system that controls aggregation of the amoeboid microorganismDictyoste-lium discoideum. The model, which is based on a classical model due to Martiel and Gold-beter [16], takes the form of a planar system of ordinary differential equations with two singularperturbation parameters which manifest very differently: while one parameter encodes the sep-aration of scales between the slow and fast variables, the other induces a non-uniformity in thecorresponding vector field in the singular limit. We apply geometric singular perturbation the-ory and the desingularisation technique known as “blow-up” to construct a family of attracting,periodic (relaxation-type) orbits; in the process, we elucidate the novel singular structure ofthe model, and we describe in detail the resulting oscillatory dynamics.
Original languageEnglish
Number of pages33
JournalJournal of mathematical analysis and applications
Volume483
Issue number1
Early online date11 Oct 2019
DOIs
Publication statusPublished - 1 Mar 2020

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