Skip to main content

Neurons are poised near the edge of chaos

Chua, Leon O., Sbitnev, Valery, Hyongsuk, Kim (2012) Neurons are poised near the edge of chaos. International Journal of Bifurcation and Chaos, 22 (04). 1250098- 1. ISSN 0218-1274. (doi:10.1142/S0218127412500988) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1142/S0218127412500988

Abstract

This paper shows the action potential (spikes) generated from the Hodgkin-Huxley 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 × 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.

Item Type: Article
DOI/Identification number: 10.1142/S0218127412500988
Uncontrolled keywords: *CHAOS theory *NEURONS *EIGENVALUES *JACOBIAN matrices *NONLINEAR differential equations *ACTION potentials (Electrophysiology) *HOPF bifurcations
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QC Physics
Divisions: Faculties > Sciences > School of Computing
Depositing User: Stewart Brownrigg
Date Deposited: 07 Mar 2014 00:05 UTC
Last Modified: 29 May 2019 12:20 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/40164 (The current URI for this page, for reference purposes)
  • Depositors only (login required):