Size-Structured Population Models of Daphnia with Several Algae Resources and Unification by Characteristic Equations

2021 ◽  
Author(s):  
Mohamed El-Doma
Keyword(s):  
Population Models ◽  
Characteristic Equations ◽  
Structured Population Models ◽  
Structured Population

scholarly journals On the formulation and analysis of general deterministic structured population models

2001 ◽  
Vol 43 (2) ◽  
pp. 157-189 ◽  
Author(s):  
O. Diekmann ◽  
M. Gyllenberg ◽  
H. Huang ◽  
M. Kirkilionis ◽  
J.A.J. Metz ◽  
...  
Keyword(s):  
Population Models ◽  
Structured Population Models ◽  
Structured Population

scholarly journals Splitting-particle methods for structured population models: Convergence and applications

2014 ◽  
Vol 24 (11) ◽  
pp. 2171-2197 ◽  
Author(s):  
J. A. Carrillo ◽  
P. Gwiazda ◽  
A. Ulikowska
Keyword(s):  
Numerical Scheme ◽  
Order Of Convergence ◽  
Operator Splitting ◽  
Population Models ◽  
Particle Simulation ◽  
Particle Methods ◽  
Test Cases ◽  
Structured Population Models ◽  
Convergence Error ◽  
Structured Population

We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used in biology, which is in essence an analogue of particle methods used in physics. Our method exploits the split-up technique, thanks to which the transport step and the nonlocal integral terms in the equation can be separately considered. The order of convergence of the proposed method is obtained in the natural space of finite non-negative Radon measures equipped with the flat metric. This convergence is studied even adding reconstruction and approximation steps in the particle simulation to keep the number of approximation particles under control. We validate our scheme in several test cases showing the theoretical convergence error. Finally, we use the scheme in situations in which the EBT method does not apply showing the flexibility of this new method to cope with the different terms in general structured population models.

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