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Hearts are Poised Near the Edge of Chaos

School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, P. R. China

School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China

E-mail Address: zhengze_wu@foxmail.com

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Leon Chua

Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA

TUM Affiliated Distinguished Professor, Fakultat für Elektrotechnik und Informationstechnik, Technische Universität München, Arcisstrasse 21, 80333 München, Germany

E-mail Address: chua@eecs.berkeley.edu

Corresponding author.

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https://doi.org/10.1142/S0218127420300232Cited by:13 (Source: Crossref)

Abstract

The Cardiac Purkinje Fiber (CPF) is the last branch of the heart conduction system, which is meshed with the normal ventricular myocyte. Purkinje fiber plays a key role in the occurrence of ventricular arrhythmia and maintenance. Does the heart Purkinje fiber cells have the same memory function as the cerebral nerve? In this paper, the cardiac Hodgkin–Huxley equation is taken as the object of study. In particular, we find that the potassium ion-channel $K$ and the sodium ion-channel $N a$ are memristors. We also derive the small-signal equivalent circuits about the equilibrium points of the CPF Hodgkin–Huxley model. According to the principle of local activity, the regions of Locally-Active domain, Edge of Chaos domain and Locally-Passive domain are partitioned under parameters $(a, b)$ , and the domain exhibiting the normal human heartbeat frequency range (Goldilocks Zone) is identified. Meanwhile, the Super-Critical Hopf bifurcation of the CPF Hodgkin–Huxley model is identified. Finally, the migration changes between different state domains under external current $I_{ext}$ excitation are analyzed in detail.

All of the above complex nonlinear dynamics are distilled and mapped geometrically into a surreal union of intersecting two-dimensional manifolds, dubbed the Hodgkin–Huxley’smagic roof.

Keywords:

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