Limit Cycles and Bifurcations in a Biological Clock Model
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 . 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.
Keywordslimit cycle bifurcation circadian rhythm model
Unable to display preview. Download preview PDF.
- 4.Nagy, B.: Comparison of the bifurcation curves of a two-variable and a three-variable circadian rhythm model. Appl. Math. Modelling (under publication)Google Scholar