Two stable resting potentials in a mathematical model of a non-pacemaker cardiac cell

Summary form only given. The equilibrium solutions of a nonpacemaker cell were followed when the intensity (I) of an added steady depolarizing bias current was varied. The nonpacemaker cell was mathematically described with the two-state-variables model of Van Capelle and Durrer. Experimental confirmation of hysteresis phenomena of the type first predicted when using this model demonstrated that it can provide interesting clues for the explanation of some cardiac rhythm disturbances. For decreasing values of I, the nonpacemaker cell behaviour can be classified according to the following patterns: for large values of I, the cell has only one stable stationary solution; for values of I between two critical values I_HB and I_1p2 , corresponding to a Hopf bifurcation point and a turning point, the cell is stable with two levels of stable resting potential, coexisting with an unstable stationary solution; and for values of I between a second turning point I_lp1 and I_HB, one stable stationary solution coexists with a stable limit cycle giving rise to annihilation phenomena