# Marine population dynamics problem

Marine population dynamics problem
Algebraic states: $n_s$
Continuous control values: $2 n_s$
Path constraints: $4 n_s$

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

$\begin{array}{llcl} \displaystyle \min_{g, m} & \sum\limits_{j=1}^{n_s} &&||y(\tau_j; g, m) - z_j||^2 \\[1.5ex] \mbox{s.t.} & \dot{y}_j & = & g_{j-1} y_{j-1} - (m_j + g_j) y_j \qquad \forall j \in 1, ..., n_s,\\ & g_j, m_j &\in& [0,1]. \end{array}$

where $g_j$ and $m_j$ are the growth and mortality rates at stage $j$ respectively and the initial conditions are unknown. The error between computed and observed data is minimized.

## Parameters

There are $n_s$ stages and $n_m$ timepoints at which the error is minimized.

## Source Code

Model descriptions are available in