12 pm Thursday, 10 May, 2012
303-412
| 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 models. |