12 pm Thursday, 10 May, 2012
|Excitable systems of reaction-diffusion equations are used|
to model many biophysical processes, including changes of
intracellular calcium concentration in various cell types.
Intracellular calcium plays an important role in many cells, being
involved in the process of delivering external signals to the inside
of the cell. Signaling is thought to occur in many cases via
oscillation of the calcium concentration inside the cell.
It is known that the dynamics of many mathematical models of
intracellular calcium is strongly influenced by the presence of global
bifurcations, including homoclinic and heteroclinic bifurcations of
periodic orbits. Using a simple calcium model, we illustrate a
numerical method, based on Lin's approach, for finding and continuing
heteroclinic connections between periodic orbits. Locating such
bifurcations helps to understand the overall bifurcation structure of
calcium dynamics. This approach can also apply to other excitable