Bifurcation structure of a periodically driven nerve pulse equation modelling cardiac conduction

A novel quiescent nerve pulse equation has been used to model cardiac trans membrane action potential propagation. The bifurcation structure of this eq uation driven by a periodic train of Dirac delta spikes, modelling experime ntal action potential measurements, displays a complicated transition regio n which connects a conventional region of fully developed period doubling c ascades to a conventional region of Arnold tongues. Within the transition r egion multistability is frequently encountered. Lyapunov exponents, winding numbers and firing rate maps are presented in dependence on amplitude-freq uency parameters of driving. The rich variety of calculated arrhythmias and conduction blocks agrees well with measured behaviour of animal Purkinje f ibres. (C) 1999 Elsevier Science Ltd. All rights reserved.