Glossary
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| Abel, Niels | Niels Henrik Abel (1802--1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. |
| Abel's formula | Abel's formula or Abel's identity is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation. |
| Zeeman model |
In 1972 (Zeeman, E.C.: Differential Equations and Nerve Impulse. Towards a Theoretical Biology, 4, pp. 8-67), Zeeman presented an important set of nonlinear dynamical equations for
heartbeat modelling, based on the Van der Pol-Lienard equation.
\[
\begin{split}
\varepsilon\,\frac{{\text d}x}{{\text d}t} &= T\, x - x^3 - y, \quad T > 0,
\\
\frac{{\text d}y}{{\text d}t} &= x - x_d .
\end{split}
\]
Here variable x represents the length of a muscle fiber in the heart
and the variable y is an electrical control variable that triggers the
electro-chemical wave leading to the heart contraction.
The positive constant T represents a tension of muscle and is related
to blood pressure. The constant ε characterizes the heart. The initial conditions are usualy taken as x(0) = 1 and y(0) = 0.
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