Biological Oceanography

%3. Set Parameters

a=0.69; b=0.06; c=0.02; d=0.5;  e=0.03;

%reduce parameters  for small   time    steps

as=a/nsteps;    bs=b/nsteps;    cs=c/nsteps;    

ds=d/nsteps;    es=e/nsteps;    ct  =   0;

%4. Main    daily   loop

for i=1:ndays

%Variant    2:  Remove  next    “%” to

%   randomly    vary a (0.52    to  0.86)

%as= a*(1.+ 0.5*(rand-0.5))/nsteps;

%5. “Euler” loop    to  closely track   the

%   solution:

    for j=1:nsteps

            ct  =   ct+1;

            T(ct)=ct/nsteps;

            P(ct)=PP;   Z(ct)=ZZ;

            dP=as*PP-bs*PP*ZZ;

            dZ=cs*PP*ZZ-ds*ZZ;

%   Variant 2:  Remove  next    “%” to  add

%   grazer  cannibalism

%dZ=dZ-es*ZZ*ZZ;

            PP=PP+dP;   ZZ=ZZ+dZ;   

    end

end

%Graph  result

figure;

plot(T(1:end),P(1:end),′g′);    hold    on

plot(T(1:end),Z(1:end),′r′);

axis([0 60  0   100]);

(^) Same instructions as at bottom of Box 4.1.
Fig. 4.2 (a) Persistent oscillations of a Lotka–Volterra model of phytoplankton–grazer
interaction with no damping process, plotted as a time-series. (b) The same
phytoplankton–grazer relationship, but with the grazers slightly self-limiting (a
quadratic damper term added). (c) Exactly like (b), but with random variation of the
phytoplankton growth rate.