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Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

A note on semi-discrete modelling in the life sciences.

Ludovic Mailleret¹, Valérie Lemesle

¹Institut National de Recherche Agronomique, Unité de Recherche 880, 06903 Sophia Antipolis, France. ludovic.mailleret@sophia.inra.fr

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|November 4, 2009

Summary

Semi-discrete models, a hybrid dynamical system type, are crucial in life sciences for population dynamics. This study introduces these models using examples like the Beverton and Holt model and Allee effects.

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Area of Science:

Ecology
Mathematical Biology
Population Dynamics

Background:

Semi-discrete models are hybrid dynamical systems featuring continuous dynamics punctuated by discrete events.
These models have a significant history in life sciences, notably in population dynamics since the Beverton and Holt model (1957).

Purpose of the Study:

To provide a comprehensive introduction to semi-discrete modeling.
To illustrate applications with two key examples: the Beverton and Holt model and a novel immigration model with Allee effect.

Main Methods:

Recalling the foundational Beverton and Holt population dynamics model.
Developing an original semi-discrete model for population immigration under a strong Allee effect.

Main Results:

The study demonstrates the utility of semi-discrete models through detailed examples.
It highlights their applicability in understanding complex ecological phenomena like Allee effects.

Conclusions:

Semi-discrete models offer a powerful framework for analyzing biological systems with intermittent changes.
The presented examples showcase their versatility and importance in life science research.