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Bifurcation structure of a periodically driven nerve pulse equation modelling cardiac conduction. (English) Zbl 0967.92007

Summary: 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.

MSC:

92C30 Physiology (general)
92C20 Neural biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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