On the chaotic pole of attraction for Hindmarsh-Rose neuron dynamics with external current input

Emile Franck Doungmo Goufo, Conrad B. Tabi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Since the neurologists Hindmarsh and Rose improved the Hodgkin-Huxley model to provide a better understanding on the diversity of neural response, features like pole of attraction unfolding complex bifurcation for the membrane potential was still a mystery. This work explores the possible existence of chaotic poles of attraction in the dynamics of Hindmarsh-Rose neurons with an external current input. Combining with fractional differentiation, the model is generalized with the introduction of an additional parameter, the non-integer order of the derivative σ , and solved numerically thanks to the Haar Wavelets. Numerical simulations of the membrane potential dynamics show that in the standard case where the control parameter σ = 1, the nerve cell’s behavior seems irregular with a pole of attraction generating a limit cycle. This irregularity accentuates as σ decreases (σ = 0.9 and σ = 0.85) with the pole of attraction becoming chaotic.
Original languageEnglish
Article number023104
Pages (from-to)1-9
Number of pages9
JournalChaos (Woodbury, N.Y.)
Volume29
Publication statusPublished - 2019

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neurons
Neurons
attraction
Pole
Neuron
Poles
poles
Membrane Potential
membranes
Membranes
Haar Wavelet
nerves
Irregularity
Unfolding
Nerve
irregularities
Limit Cycle
Control Parameter
Irregular
Fractional

Cite this

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title = "On the chaotic pole of attraction for Hindmarsh-Rose neuron dynamics with external current input",
abstract = "Since the neurologists Hindmarsh and Rose improved the Hodgkin-Huxley model to provide a better understanding on the diversity of neural response, features like pole of attraction unfolding complex bifurcation for the membrane potential was still a mystery. This work explores the possible existence of chaotic poles of attraction in the dynamics of Hindmarsh-Rose neurons with an external current input. Combining with fractional differentiation, the model is generalized with the introduction of an additional parameter, the non-integer order of the derivative σ , and solved numerically thanks to the Haar Wavelets. Numerical simulations of the membrane potential dynamics show that in the standard case where the control parameter σ = 1, the nerve cell’s behavior seems irregular with a pole of attraction generating a limit cycle. This irregularity accentuates as σ decreases (σ = 0.9 and σ = 0.85) with the pole of attraction becoming chaotic.",
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On the chaotic pole of attraction for Hindmarsh-Rose neuron dynamics with external current input. / Doungmo Goufo, Emile Franck; Tabi, Conrad B.

In: Chaos (Woodbury, N.Y.), Vol. 29, 023104, 2019, p. 1-9.

Research output: Contribution to journalArticle

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AU - Tabi, Conrad B.

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AB - Since the neurologists Hindmarsh and Rose improved the Hodgkin-Huxley model to provide a better understanding on the diversity of neural response, features like pole of attraction unfolding complex bifurcation for the membrane potential was still a mystery. This work explores the possible existence of chaotic poles of attraction in the dynamics of Hindmarsh-Rose neurons with an external current input. Combining with fractional differentiation, the model is generalized with the introduction of an additional parameter, the non-integer order of the derivative σ , and solved numerically thanks to the Haar Wavelets. Numerical simulations of the membrane potential dynamics show that in the standard case where the control parameter σ = 1, the nerve cell’s behavior seems irregular with a pole of attraction generating a limit cycle. This irregularity accentuates as σ decreases (σ = 0.9 and σ = 0.85) with the pole of attraction becoming chaotic.

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