In matlab Loops. In the Lotka Volterra predator-prey model, the changes in the p

Question

In matlab

Loops. In the Lotka Volterra predator-prey model, the changes in the predator population y and the prey population x are described by the following equations:

xt=xt+1xt=axtbxtyt

yt=yt+1yt=cxtytdyt

Write a function simulatepredatorprey(x,y, a,b,c,d, T) that takes in the initial population sizes of x and y and simulates the model with the input parameters, for T discrete time steps (in years), updating the population sizes after each time step. For each time step, calculate the number of predator & prey from the population sizes of the previous year using the difference equations above. Your function should return the history of the population sizes as a 2-row matrix (first row containing the history of x and second row containing the history of y), starting with the initial population sizes in the first column, and with each additional column containing the population sizes of x and y at that time step.

Your function should also plot the population the predator and the prey over time. Predator and prey plots should use different line and marker styles. The axes should be labeled and the figure should contain a legend. Assume the time steps are given in years and the population sizes are given in thousands.
>> disp(simulatepredatorprey(10,20, 0.1, 0.01, 0.01, 0.2, 1))
    10     9
    20    18
>> disp(simulatepredatorprey(10,20, 0.1, 0.01, 0.01, 0.2, 5))
   10.0000    9.0000    8.2800    7.7815    7.4592    7.2791
   20.0000   18.0000   16.0200   14.1425   12.4145   10.8576

Explanation / Answer

%Define a function

function pp=simulatepredatorprey(x,y,a,b,c,d,T)

%Get value of N

N=input('Time of the whole simulation (in years) N=');

%Assign value

X(1)=x;

%Assign value

Y(1)=y;

%Assign value

xx=x;

%Assign value

yy=y;

%Assign value

t=T;

%Declare variable

i=1;

%Loop until length

for n=1:1:N

%Assign value

XX(n)=xx;

%Assign value

YY(n)=yy;

%Compute xx

xx=a*XX(n)-b*XX(n)*YY(n)+XX(n);

%Compute yy

yy=c*XX(n)*YY(n)-d*YY(n)+YY(n);

%If n equals t

if n==t

%Update i

i=i+1;

%Assign value

X(i)=xx;

%Assign value

Y(i)=yy;

%Update t

t=t+T;

%End

end

%End

end

%Assign value

pp=[X;Y];

%End

end

%Call method

disp(simulatepredatorprey(10,20,0.1,0.01,0.01,0.2,1))

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.