What Are the Physical Meanings of the Parameters in the Lotka-Volterra Model?

[sapiental]

Hello,

I have to write a program for the Lotka-Volterra model. When I researched this model online most websites gave me the following ODE's:

dx/dt = a*x - b*x*y
dy/dt = e*b*x*y - c*y

However, my book gives me the following ODE's:

dx/dt = (a - bx - cy)x
dy/dt = (-d+ex)y

and states that x reperesents the number of hares and y represents the number of foxes..

is there anyway some could help me describe the physical meaning of the parameters my book gave me?

I think...

a = the coefficent for the increase in the rabbit population due to resources
b = the natural death rate of rabbit not due to predators
c = the coefficent for the chance that the predator and prey will meet and the prey gets eaten
d = the natural death rate of predators without food
e = chance predator and prey will meet and prey gets eaten


please let me know what you think. thanks alot!

 

[cristo]

Are you sure you've copied it down from your book correctly, as i can't see the need for the term in x^2 in your dx/dt equation

 

[sapiental]

yep, I copied it correctly. That's exactly what threw me completely off as well..

here is the actual question:

Write a program using adaptive Runge-Kutta to compute the trajectory (x(t),y(t)) for a variety of initial conditions using:

a = 10
b = 10^-5
c =.1
d = 10
e = .1

Take x(0) > 0, y(0) > 0 since the number of animals should be positive..

It seems that the regular L-V model has 4 parameters where as the one in my book adds a 5th one..

 

[cristo]

My *guess* is that its a typo in your book, and the x shouldn't be there after the b in the dx/dt eqn.

This makes sense, if the variables are defined as you have written them, since it says that the rate of change of prey is equal to the natural increase of the prey (a*x) minus the natural rate of death of the prey (b*x) minus the rate that the prey gets eaten by the predator (c*x*y).

Anyway, like I said, it's just a guess!

 

[sapiental]

thanks a lot for all your input