Please provide Handwritten answer

Advanced Math

Please prove hos the stability changes for parts i) and ii), a bifurcation plot/proof is what I'm mainly looking for!

Study the local stability of the positive steady state of the following neutral logistic equation (may be a problematic population model) r'(t) = rx(t)[1 - x(t - T)] + ar'(t -7), where r, r, a are positive constants. How the stability changes when one increase i) a from 0 to oo; ii) + from 0 to co