Multiple oscillatory and steady state solutions in an excitable cardiac cell model

Abstract

The authors describe the behavior of a single cardiac element with respect to the possible transitions between automatic and steady stable states. Bifurcation techniques enabled them to classify behavior patterns in this cellular element by using the model of F.J.L. Van Capelle and D. Durrer (1980). Five behavioral pattern domains were delineated: (1) a nonautomatic zone with a single stationary stable state, (2) a zone where a steady-state solution and a pacemaker stable state coexist, (3) an automatic zone with a single oscillatory stable state, (4) an overlap between high- and low-amplitude oscillator states, and (5) a nonautomatic zone with a single steady state. In the transitional zones separatrices, represented by unstable orbits, provided a topological means of predicting the annihilation of rhythmic activity by either depolarizing or hyperpolarizing pulse of proper amplitude and proper phase. The coexistence of stable states near the two Hopf bifurcation points implies hysteresis phenomena. Consequently, small fluctuations of some parameter governing the cyclic regenerative process of transitional cells would be able to bring about burstlike intermittent activities. >