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Third-order memristive Morris-Lecar model of barnacle muscle fiber. (English) Zbl 1366.34068

Summary: 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.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
94C05 Analytic circuit theory
92C20 Neural biology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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