Abstract
A three-variable dynamical system describing the circadian oscillation of two proteins (PER and TIM) in cells is investigated. We studied the saddle-node and Hopf bifurcation curves and distinguished four cases according to their mutual position in a former article. Other bifurcation curves were determined in a simplified, two-variable model by Simon and Volford [6]. Here we show a set of bifurcation curves that divide the parameter plane into regions according to topological equivalence of global phase portraits, namely the global bifurcation diagram, for the three-variable system. We determine the Bautin-bifurcation point, and fold bifurcation of cycles numerically. We also investigate unstable limit cycles and the case when two stable limit cycles exist.
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Nagy, B. (2008). Limit Cycles and Bifurcations in a Biological Clock Model. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2007. Lecture Notes in Computer Science, vol 4818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78827-0_22
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DOI: https://doi.org/10.1007/978-3-540-78827-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78825-6
Online ISBN: 978-3-540-78827-0
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