Isle Royale National Park is a 210-square-mile archipelago composed of a single large isla...

The following script generates the solution:

h=0.0625;tspan=[1959 2020];y0=[563 20];

a=0.23;b=0.0133;c=0.4;d=0.0004;

td=[1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006];

Md=[563 610 628 639 663 707 733 765 912 1042 1268 1295 1439 1493 1435 1467 1355 1282 1143 1001 1028 910 863 872 932 1038 1115 1192 1268 1335 1397 1216 1313 1590 1879 1770 2422 1163 500 699 750 850 900 1100 900 750 540 450];

Wd=[20 22 22 23 20 26 28 26 22 22 17 18 20 23 24 31 41 44 34 40 43 50 30 14 23 24 22 20 16 12 12 15 12 12 13 17 16 22 24 14 25 29 19 17 19 29 30 30];

[t y] = rk4sys(@predprey,tspan,y0,h,a,b,c,d);

subplot(3,1,1);plot(t,y(:,1),td,Md,'o')

title('(a) Moose time series'),grid

subplot(3,1,2);plot(t,y(:,2),td,Wd,'o')

title('(b) Wolf time series'),grid

subplot(3,1,3);plot(y(:,1),y(:,2))

title('(c) Phase plane plot'),grid,xlabel('Moose'),ylabel('Wolves')

ssrM=0;ssrW=0;

for i = 1:length(td)

for j = 1:length(t)

if td(i)==t(j)

ssrM=ssrM+(Md(i)-y(j,1))^2;

ssrW=ssrW+(Wd(i)-y(j,2))^2;

end

end

end

fprintf('SSR(Moose) = %8.4g\n',ssrM)

fprintf('SSR(Wolves) = %8.4g\n',ssrW)