Marine population dynamics problem

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

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

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

• AMPL/TACO code at Marine population dynamics problem (TACO)