# [SOLVED]mutualism autonomous system

#### dwsmith

##### Well-known member
Consider two species whose survival depend on their mutual cooperation. An example would be a species of the bee that feeds primarily on the nectar of one plant species and simultaneously pollinates that plant. One simple model of this mutualism is given by the autonomous system:
\begin{align}
\frac{dx}{dt} =& -ax + bxy\notag\\
\frac{dy}{dt} =& -my + nxy\notag
\end{align}

Interpret the constants a, b, m, and n in terms of the physical problem.

In the absence of cooperation, the system would be
\begin{align}
\frac{dx}{dt} =& -ax\\
\frac{dy}{dt} =& -my\notag
\end{align}

So a and m are non-negative. So a and m are the deaths proportional to the given population?

I don't know what to say about b and n though.

#### springfan25

##### New member
for interpretation purposes is often handy to look at the rate of change per unit of existing population:

$\frac{\frac{dx}{dy}}{x}=-a +by$

so i would describe b as the increase in (proportional) growth in x per unit of y population.

similarly for n.

• dwsmith