Marine population dynamics problem
From mintOC
| Marine population dynamics problem | |
|---|---|
| State dimension: | 1 |
| Differential states: | n_2 |
The Marine population dynamics problem estimates growth and mortality rates of a marine species at each stage (for example ages or development stage) given the population as a function of time.( Problem taken from the COPS library)
Mathematical formulation
The problem is given by
![\begin{array}{llcl}
\displaystyle \min_{g, m} & \sum\limits_{j=1}^{n_m} &&||y(\tau_j; g, m) - z_j||^2 \\[1.5ex]
\mbox{s.t.}
& \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \qquad \forall j \in 1, ..., n_s,\\
& g_j, m_j &\in& [0,1].
\end{array}](https://mintoc.de/images/math/b/a/6/ba686bce5cfd80ce0f888915706e2d57.png)
where 
and 
are the growth and mortality rates at stage 
respectively and the initial conditions are unknown.
The error between computed and observed data is minimized.
Parameters
There are 
stages and 
timepoints at which the error is minimized.
Source Code
Model descriptions are available in
