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I have this ex:

dx/dt = −x(1 − y), t0 = 0, x(t0) = 0.5, (3)

dy/dt = y(1 − x), t0 = 0, y(t0) = 2 (4)

These equations are also known as Lotka-Volterra or predator-prey equations modeling evolution of species as a function of time t. In the equations above variable x stands for the number of predators, and y is the number of prey.

Let [0, 40] be the interval of integration.

Please implement improved Euler integration scheme with ∆ = 0.001, ∆ = 0.002, and

∆ = 0.005 (2) for (3) and (4). Plot the values of x(t), y(t) for t ∈ [0, 40] in the xy plane.

I have written this so far but i get an error (line 32) about ''='' . I have also tried to write it as ''=='' but it still does not work

Could someone help me?

function [x_out,y_out,t_out]=improved_euler_CS(Delta_in,T0,T)

% setting up parameters of the integration

t_max=T;

t_min=T0;

Delta=Delta_in;

% defining initial conditions

t=t_min:Delta:t_max;

% reserving space for y

x=zeros(1,size(t,2));

y=zeros(1,size(t,2));

% defining initial conditions

z=zeros(1,2);

z(1)=0.5; % this is the initial condition for x

z(2)=2; % this is the initial condition for y

for i=1:size(t,2)

x(i)=z(1);

y(i)=z(2);

z1=competing_species_rhs(z);

z2=competing_species_rhs(z+Delta*z1);

z=z+Delta*(z1+z2)/2;

end;

% returning the values of x,y, and t back to MATLAB?s environment

t_out=t;

x_out=x;

y_out=y;

where the function competing species rhs is defined as

function z_out=competing_species_rhs(z)

%create a vector for storing the results;

p=zeros(1,2);

%z(1) is supposed to store the values of x

%z(2) is supposed to store the values of y

p(1) = (-z(1)*(1=(z(2))));

p(2) = z(2)*(1=(z(1)));

z_out=p;

end

end

Fabio Freschi
on 20 Feb 2020

I think it should be "-"

p(1) = (-z(1)*(1-(z(2))));

p(2) = z(2)*(1-(z(1)));

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