Bifurcation Structure of a Periodically Driven Nerve Pulse Equation Modelling Cardiac Conduction

A novel quiescent nerve pulse equation has been used to model cardiac transmembrane action potential propagation. The bifurcation structure of this equation driven by a periodic train of Dirac delta spikes, modelling experimental action potential measurements, displays a complicated transition region which connects a conventional region of fully developed period doubling cascades to a conventional region of Arnold tongues. Within the transition region multistability is frequently encountered. Lyapunov exponents, winding numbers and firing rate maps are presented in dependence on amplitude-frequency parameters of driving. The rich variety of calculated arrhythmias and conduction blocks agrees well with measured behaviour of animal Purkinje fibres. © 1999 Elsevier Science Ltd. All rights reserved.