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[SOLVED] mutualism autonomous system

dwsmith

Well-known member
Feb 1, 2012
1,673
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
Mar 3, 2012
14
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.