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Memristive Model of the Barnacle Giant Muscle Fibers

Maheshwar Pd. Sah

Department of Electrical and Computer Engineering, Purdue University Fort Wayne, Fort Wayne IN 46805, USA

Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Jeonbuk 561-756, South-Korea

E-mail Address: sahm@ipfw.edu

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Hyongsuk Kim

Division of Electronics and Information Engineering, Chonbuk National University, Jeonju, Jeonbuk 561-756, South-Korea

E-mail Address: hskim@jbnu.ac.kr

Corresponding author

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Abdullah Eroglu

Department of Electrical and Computer Engineering, Purdue University Fort Wayne, Fort Wayne IN 46805, USA

E-mail Address: eroglua@ipfw.edu

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, and

Leon Chua

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

Fakultat fur Elektrotechnik und Informationstechnik, Technische Universität München, Arcisstrasse 21, 80333 München, Germany

E-mail Address: chua@berkeley.edu

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https://doi.org/10.1142/S0218127416300019Cited by:17 (Source: Crossref)

Abstract

The generation of action potentials (oscillations) in biological systems is a complex, yet poorly understood nonlinear dynamical phenomenon involving ions. This paper reveals that the time-varying calcium ion and the time-varying potassium ion, which are essential for generating action potentials in Barnacle giant muscle fibers are in fact generic memristors in the perspective of electrical circuit theory. We will show that these two ions exhibit all the fingerprints of memristors from the equations of the Morris–Lecar model of the Barnacle giant muscle fibers. This paper also gives a textbook reference to understand the difference between memristor and nonlinear resistor via analysis of the potassium ion-channel memristor and calcium ion-channel nonlinear resistor. We will also present a comprehensive in-depth analysis of the generation of action potentials (oscillations) in memristive Morris–Lecar model using small-signal circuit model and the Hopf bifurcation theorem.

Keywords:

References

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