function dy = LotkaVolterra_eqn(t,y)
global r1 r2 k1 k2 beta12 beta21
dy = zeros(2,1); % need to be a column vector
dy(1) = r1*y(1)*(k1-y(1)-beta12*y(2))/k1;
dy(2) = r2*y(2)*(k2-y(2)-beta21*y(1))/k2;