The Effect Of Ion Pumps On The Behaviour Of Travelling Waves In The Fire-diffuse-fire Model

In this thesis,we explicitly analyse the effect of calcium pumps which drive Ca2+from the cytosol back into the endoplasmic,especially the effect of pumps on the the behaviour of travelling waves in the fire-diffuse-fire model(i.e.,FDF).We first provide the FDF model and introduce some parameter symbols discussed in this thesis.For trav-elling waves,in which release events occur sequentially,we construct the speed of waves as a function of system parameters.After discussing the effect of the decay term on the FDF model,we conclude that a finite decay term can lead to co-existence of solution-s.Then we analyze the linear stability of the solution branch.The decay term may also cause(single release saltatory wave)propagation failure.We discuss the continuum lim-it of the FDF model and perform similar analyzes on the stability of the solution.At the same time,we show that the saltatory waves do not propagate with a constant profile,whereas the traveling pulses can propagate with constant profile.