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

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Homework Help Overview

The discussion revolves around the Lotka-Volterra model, which describes the dynamics of predator-prey interactions. The original poster presents two different sets of ordinary differential equations (ODEs) for the model and seeks clarification on the physical meanings of the parameters in the version provided by their book.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to identify the meanings of parameters in their book's version of the Lotka-Volterra model. Some participants question the accuracy of the equations presented, particularly regarding the presence of a term in the dx/dt equation. Others suggest that there may be a typographical error in the book.

Discussion Status

The discussion is ongoing, with participants exploring the implications of the different parameter sets. Some guidance has been offered regarding the interpretation of the parameters, but no consensus has been reached on the correctness of the equations.

Contextual Notes

The original poster notes specific values for the parameters and constraints on initial conditions, emphasizing the requirement for positive animal populations. There is uncertainty regarding the inclusion of an additional parameter in the book's equations compared to the standard model.

sapiental
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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 coefficient for the increase in the rabbit population due to resources
b = the natural death rate of rabbit not due to predators
c = the coefficient 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 a lot!
 
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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
 
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..
 
Last edited:
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!
 
thanks a lot for all your input
 

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