Writing a differential equation for iteration using for loop.

I have a differential equation:

p=@(t,x,y) (a-x^2-y^2)*x-omega*y;

Why for iteration we write this equation as ?

for i=2:50000
                x(i)=x(i-1)+((a-x(i-1)^2-y(i-1)^2)*x(i-1)-omega*y(i-1))*dt;
end

Answer 1

[Alan Stevens]

This is known as simple Euler integration. It arises from

% dx/dt = (a - x^2 - y^2)*x - omega*y   

% Let dx/dt be approximated by (x(t+dt) - x(t))/dt
% and the right hand side by (a - x(t)^2 - y(t)^2)*x(t) - omega*y(t)

% so (x(t+dt) - x(t))/dt = (a - x(t)^2 - y(t)^2)*x(t) - omega*y(t)        approximately

% Multiply both sides by dt to get
% x(t+dt) - x(t) = ((a - x(t)^2 - y(t)^2)*x(t) - omega*y(t))*dt

% Add x(t) to both sides to get
% x(t+dt) = x(t) + ((a - x(t)^2 - y(t)^2)*x(t) - omega*y(t))*dt

[Heya :)]

Thank you for the detailed explanation.