Write a FORTRAN program which PROBLEM 24 - 0590: uses the modified Euler method to simulate the competition of two species of population, N7 (t) and N2(t), isolated from the environment, from time t = 0 to t = tf, if it is observed that: N1 = (A1 - K11N1 - K12N2) (1) N2 = (A2 - K21N1 - K22N2) (2) where N,N2 are the time rates of N1 N1 change of N1(t) and N2(t), respectively. A, and A2 are positive constants involving natural birth/death rates for each species when isolated. The Kij are positive constants involving cross-effects between species. Initially, N1(0) = N10, and %3D N2(0) = N20 -

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PROBLEM 24 - 0590:
uses the modified Euler
Write a FORTRAN program which
method to simulate the
competition of two species of
population, N1 (t) and N2(t),
isolated from the environment,
from time t = 0 to t = tf, if it is
observed that:
N1 = (A1 - K11N1 - K12N2)
(1)
N2 = (A2 - K21N, - K22N2)
(2)
where N,N, are the time rates of
%3D
N1
%D
N1
change of N1(t) and N2(t),
respectively. A, and A2 are positive
constants involving
natural birth/death rates for each
species when isolated. The
Ki j are positive constants involving
cross-effects between
species. Initially, N1(0) = N10, and
%3D
N2(0) = N20 -
Transcribed Image Text:PROBLEM 24 - 0590: uses the modified Euler Write a FORTRAN program which method to simulate the competition of two species of population, N1 (t) and N2(t), isolated from the environment, from time t = 0 to t = tf, if it is observed that: N1 = (A1 - K11N1 - K12N2) (1) N2 = (A2 - K21N, - K22N2) (2) where N,N, are the time rates of %3D N1 %D N1 change of N1(t) and N2(t), respectively. A, and A2 are positive constants involving natural birth/death rates for each species when isolated. The Ki j are positive constants involving cross-effects between species. Initially, N1(0) = N10, and %3D N2(0) = N20 -
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