Complex nonlinear dynamics of the Hodgkin-Huxley equations induced by timescale changes

The Hodgkin-Huxley equations with a slight modification are investigated, i n which the inactivation process (h) of sodium channels or the activation p rocess of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau pot ential, such as in heart muscle cells, to chaotic bursting firings. When h is slowed down-differently from the case of nz variable being slow-chaotic bursting oscillations are observed for a wide range of parameter values alt hough both variables cause a decrease in the membrane potential. The underl ying nonlinear dynamics of various action potentials are analyzed using bif urcation theory and a so-called slow-fast decomposition analysis. It is sho wn that a simple topological property of the equilibrium curves of slow and fast subsystems is essential to the production of chaotic oscillations, an d this is the cause of the large difference in global firing characteristic s between the h-slow and n-slow cases.