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## Main Question or Discussion Point

I want to show, in a talk, how to build the Predator-Prey (Lotka Volterra) model. It starts off with the "Population Law of Mass Action" i.e. "At time t the rate of change of one population due to interaction with another is proportional to the product of the two populations at that time t"

Is it an abuse of notation to write this (for populations x (predator) and y(the prey)) as:

##\frac{dx}{dt} \propto xy ##

##\frac{dy}{dt} \propto xy ##

I think it's ok, I've just never seen this written for a differential equation.

The next step would be to write:

##\frac{dx}{dt} = axy ##

##\frac{dy}{dt} = bxy ##

For some a and b, then start showing what happens when x starts eating y.

-Dave K

Is it an abuse of notation to write this (for populations x (predator) and y(the prey)) as:

##\frac{dx}{dt} \propto xy ##

##\frac{dy}{dt} \propto xy ##

I think it's ok, I've just never seen this written for a differential equation.

The next step would be to write:

##\frac{dx}{dt} = axy ##

##\frac{dy}{dt} = bxy ##

For some a and b, then start showing what happens when x starts eating y.

-Dave K