Rabbit vs. Foxes

[Eddie W. Shore]

The program presented today is based on the Rabbits vs. Foxes program for the HP 25 (see source below). The program determines the population of rabbits and foxes over time as modeled by the differential equations:

Change in Rabbits:
dr/dt = 2 * r - α * r * f

Change of Foxes:
df/dt = -f + α * r * f

where:
r = population of rabbits
f = population of foxes
α = probability of a rabbit encounters a fox
h = step

This is approximated by Euler's method.

The HP Prime program RABBIT25 displays a print screen of results of the desired amount of iterations. The HP 42S program RAB25 displays the results one step at time in the format rrrrr.fffff (rabbits.foxes), like the original HP 25 program.

HP Prime Program RABBIT25

Code:


EXPORT RABBIT25()
BEGIN
// 2020-01-20 EWS
// Based on the Rabbits vs
// Foxes HP 25 program
LOCAL α,h,r,f,k,n,a;

// initialize and input
INPUT({α,h,r,f,n},
"Rabbits vs Foxes",
{"α: ","h: ","r0:","f0:","n: "},
{"α","h","inital # rabbits",
"initial # foxes",
"# iterations"});
L0:={r}; L1:={f};


// compute data
MSGBOX("L0 = rabbit population,
L1 = fox population;
(0,1,2,...,n), size n+1");
HFormat:=0;
PRINT();
PRINT("Rabbits vs Foxes");
FOR k FROM 0 TO n DO
IF k≠0 THEN
a:=α*r*f;
r:=r+h*(2*r-a);
f:=f+h*(−f+a);
END;
PRINT(k+" R: "+IP(r)+" F: "+
IP(f));
END;


// end of program
END;

Source:

Randall B. Neff and Lynn Tilman "An Example of HP-25 Programming" Hewlett-Packard Journal: November 1975. pg. 6


Blog Post: http://edspi31415.blogspot.com/2020/02/h...foxes.html