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
