GENERATION OF PERIODIC AND CHAOTIC BURSTING IN AN EXCITABLE CELL MODEL

There are interesting oscillatory phenomena associated with excitable cells that require theoretical insight. Some of these phenomena are: t he threshold low amplitude oscillations before bursting in neuronal ce lls, the damped burst observed in muscle cells, the period-adding bifu rcations without chaos in pancreatic beta-cells, chaotic bursting and beating in neurons, and inverse period-doubling bifurcation in heart c ells. The three variable model formulated by Chay provides a mathemati cal description of how excitable cells generate bursting action potent ials. This model contains a slow dynamic variable which forms a basis for the underlying wave, a fast dynamic variable which causes spiking, and and the membrane potential which is a dependent variable. In this paper, we use the Chay model to explain these oscillatory phenomena. The Poincare return map approach is used to construct bifurcation diag rams with the 'slow' conductance (i.e., g(K,C)) as the bifurcation par ameter. These diagrams show that the system makes a transition from re petitive spiking to chaotic bursting as parameter g(K,C) is varied. De pending on the time kinetic constant of the fast variable (lambda(n)), however, the transition between burstings via period-adding bifurcati on can occur even without chaos. Damped bursting is present in the Cha y model over a certain range of g(K,C) and lambda(n). In addition, a t hreshold sinusoidal oscillation was observed at certain values of g(K, C) before triggering action potentials. Probably this explains why the neuronal cells exhibit low-amplitude oscillations before bursting.