Consider the delayed logistic equation (a) Change the equation to a two-dimensional system. (b) Show that for µ > 1, there exists a nontrivial positive fixed point. (c) Show that for µ = 2, the...

Consider the delayed logistic equation

(a) Change the equation to a two-dimensional system.

(b) Show that for µ > 1, there exists a nontrivial positive fixed point.

(c) Show that for µ = 2, the nontrivial fixed point undergoes a NeimarkSacker bifurcation.

(d) Draw a phase space diagram for the system for

i. µ

ii. µ = 2.

iii. µ > 2.