Third-Order Memristive Morris-Lecar Model of Barnacle Muscle Fiber

被引：20

作者：

Rajamani, Vetriveeran ^{[1
]}

Sah, Maheshwar P. D. ^{[2
]}

Mannan, Zubaer Ibna ^{[1
]}

Kim, Hyongsuk ^{[3
]}

Chua, Leon ^{[4
]}

机构：

[1] Chonbuk Natl Univ, Div Elect & Informat Engn, Jeonju 54896, Jeonbuk, South Korea

[2] Ivy Tech Community Coll, Sch Appl Sci & Engn Technol, South West, IN 47710 USA

[3] Chonbuk Natl Univ, Div Elect Engn, Jeonju 54896, Jeonbuk, South Korea

[4] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2017年 / 27卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Morris-Lecar model; Hodgkin-Huxley model; giant barnacle muscle fiber; calcium and potassium ion-channel memristor; small unstable limit cycle oscillations; small-signal circuit model; local activity; edge of chaos; limit cycle oscillation; subcritical Hopf bifurcation; basin of attraction; action potential; MEMBRANE; CALCIUM;

D O I：

10.1142/S0218127417300154

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper presents a detailed analysis of various oscillatory behaviors observed in relation to the calcium and potassium ions in the third-order Morris-Lecar model of giant barnacle muscle fiber. Since, both the calcium and potassium ions exhibit all of the characteristics of memristor fingerprints, we claim that the time-varying calcium and potassium ions in the third-order Morris-Lecar model are actually time-invariant calcium and potassium memristors in the third-order memristive Morris-Lecar model. We confirmed the existence of a small unstable limit cycle oscillation in both the second-order and the third-order Morris-Lecar model by numerically calculating the basin of attraction of the asymptotically stable equilibrium point associated with two subcritical Hopf bifurcation points. We also describe a comprehensive analysis of the generation of oscillations in third-order memristive Morris-Lecar model via small-signal circuit analysis and a subcritical Hopf bifurcation phenomenon.

引用

页数：58

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