{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T20:59:38Z","timestamp":1763499578799},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:p> 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\u2013Huxley equation is taken as the object of study. In particular, we find that the potassium ion-channel [Formula: see text] and the sodium ion-channel [Formula: see text] are memristors. We also derive the small-signal equivalent circuits about the equilibrium points of the CPF Hodgkin\u2013Huxley 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 [Formula: see text], and the domain exhibiting the normal human heartbeat frequency range (Goldilocks Zone) is identified. Meanwhile, the Super-Critical Hopf bifurcation of the CPF Hodgkin\u2013Huxley model is identified. Finally, the migration changes between different state domains under external current [Formula: see text] excitation are analyzed in detail. <\/jats:p><jats:p> All of the above complex nonlinear dynamics are distilled and mapped geometrically into a surreal union of intersecting two-dimensional manifolds, dubbed the Hodgkin\u2013Huxley\u2019s magic roof. <\/jats:p>","DOI":"10.1142\/s0218127420300232","type":"journal-article","created":{"date-parts":[[2020,8,9]],"date-time":"2020-08-09T16:36:20Z","timestamp":1596990980000},"page":"2030023","source":"Crossref","is-referenced-by-count":16,"title":["Hearts are Poised Near the Edge of Chaos"],"prefix":"10.1142","volume":"30","author":[{"given":"Xiaohong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengze","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leon","family":"Chua","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA"},{"name":"TUM Affiliated Distinguished Professor, Fakultat f\u00fcr Elektrotechnik und Informationstechnik, Technische Universit\u00e4t M\u00fcnchen, Arcisstrasse 21, 80333 M\u00fcnchen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,8,5]]},"reference":[{"key":"S0218127420300232BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2013.2256171"},{"key":"S0218127420300232BIB002","volume-title":"Introduction to Nonlinear Network Theory","author":"Chua L. 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