{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T07:20:45Z","timestamp":1778743245425,"version":"3.51.4"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,4]]},"abstract":"<jats:p> This paper shows the action potential (spikes) generated from the Hodgkin\u2013Huxley equations emerges near the edge of chaos consisting of a tiny subset of the locally active regime of the HH equations. The main result proves that the eigenvalues of the 4 \u00d7 4 Jacobian matrix associated with the mathematically intractable system of four nonlinear differential equations are identical to the zeros of a scalar complexity function from complexity theory. Moreover, we show the loci of a pair of complex-conjugate zeros migrate continuously as a function of an externally applied DC current excitation emulating the net synaptic excitation current input to the neuron. In particular, the pair of complex-conjugate zeros move from a subcritical Hopf bifurcation point at low excitation current to a super-critical Hopf bifurcation point at high excitation current. The spikes are generated as the excitation current approaches the vicinity of the edge of chaos, which leads to the onset of the subcritical Hopf bifurcation regime. It follows from this in-depth qualitative analysis that local activity is the origin of spikes. <\/jats:p>","DOI":"10.1142\/s0218127412500988","type":"journal-article","created":{"date-parts":[[2012,5,21]],"date-time":"2012-05-21T06:30:43Z","timestamp":1337581843000},"page":"1250098","source":"Crossref","is-referenced-by-count":154,"title":["NEURONS ARE POISED NEAR THE EDGE OF CHAOS"],"prefix":"10.1142","volume":"22","author":[{"given":"LEON","family":"CHUA","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VALERY","family":"SBITNEV","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA 94720, USA"},{"name":"St. Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, Gatchina, Leningrad district, 188350, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HYONGSUK","family":"KIM","sequence":"additional","affiliation":[{"name":"Division of Electronics Engineering, Chonbuk National University, Jeonju, Jeonbuk, 561-756, South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,23]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59281-2"},{"key":"rf2","volume-title":"Introduction to Nonlinear Network Theory","author":"Chua L. 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