## Mathematics & Science
Learning Center |
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## Applications of Systems of Differential Equations## Predator-Prey Problems
The Lotka-Volterra system:
is said to be ?NDSolve NDSolve[ for the function eqnsy with the independent variable x in the range x to _{min}x. _{max}NDSolve[ eqns,y,{x,x},{_{min},x_{max}t,t}] finds a numerical solution to the partial differential equations _{min},t_{max}eqns. NDSolve[ eqns,{y{_{1},y_{2},…},x,x}] finds numerical solutions for the functions _{min},x_{max}y. >>_{i}As we have already seen, when we're dealing with a Well the initial conditions are simply the two original population sizes. Let's say that there were originally 300 rabbits and 150 foxes. This translates into the initial conditions: *r*(0) = 300*f*(0) = 150
Putting these together with the original system of differential equations, we
have everything we need to enter into the NDSolve command.
Whoops! No we don't! We also need to specify an interval upon which the
numerical solution is to be found. Let's use 0 ≤ If we want to read the answer into the variable
Go ahead—enter and evaluate it! You can switch to Mathematica by clicking on the button at left. This will
open up a fresh notebook for you. Remember that it will take it a while to start
up! Don't forget to come back here when you're done! See you in a few
minutes.Now let's go see what you should have gotten... |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |