Coexisting Behavior and Status Transition of the Hodgkin-Huxley Cardiac Purkinje Fiber Model Under External AC Injection

Abstract The membrane current $$I_m$$ I m of the Hodgkin-Huxley (HH) cardiac Purkinje fiber (CPF) model is usually calculated as direct (DC). In this paper, a conventional alternating (AC) used, namely $$I_{AC} = \textrm{Asin}(2 \pi ft)$$ AC = Asin ( 2 π f t ) , impressed injection. Dynamic characters with different AC parameters and various initial conditions are observed through phase plane orbits, waveforms, bifurcation diagrams, Lyapunov exponent spectra, which reveal multiple coexisting action potential patterns, corresponding to attractors same or periods in diagram. Meanwhile, undergoes period, quasi-period local forward inverse period-doubling bifurcations changes amplitude A frequency f further proves complex nonlinear property AC-injected model. addition, by changing external sodium-ion potassium-ion equilibrium potentials, i.e. $$E_{Na}$$ E Na $$E_{K}$$ K respectively, regularity CPF heartbeat observed. state transformations found between normal, abnormal sudden arrest, method adjusting from dangerous normal range investigated. This study may provide reference for exploring evolution dynamics HH protecting health life heart.