Difference between revisions of "Marine population dynamics problem"
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{{Dimensions | {{Dimensions | ||
| − | | | + | |nz = <math> n_s </math> |
| − | | | + | |np = <math> 2 n_s </math> |
| + | |nc = <math> 4 n_s </math> | ||
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| − | \displaystyle \min_{ | + | \displaystyle \min_{g, m} & \sum\limits_{j=1}^{n_s} &&||y(\tau_j; g, m) - z_j||^2 \\[1.5ex] |
\mbox{s.t.} | \mbox{s.t.} | ||
| − | & \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \ | + | & \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]. | & g_j, m_j &\in& [0,1]. | ||
\end{array} | \end{array} | ||
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[[Category:MIOCP]] | [[Category:MIOCP]] | ||
[[Category:ODE model]] | [[Category:ODE model]] | ||
| + | [[Category:Population dynamics]] | ||
Latest revision as of 09:31, 27 July 2016
| Marine population dynamics problem | |
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| Algebraic states: |
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| Continuous control values: |
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| Path constraints: |
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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_s} &&||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/a/a/5/aa54649329dc309f2284e509e6e5abc1.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
