Wright's Equation

Wright's equation is the nonlinear delay differential equation (Wright 1955)

(1)

where primes denote derivatives with respect to time , , and the delay is one time unit. Substituting gives the equivalent form

(2)

for . Wright studied this equation following a suggestion by Lord Cherwell (Wright 1955). Linearization at the equilibrium point gives , with characteristic equation

(3)

At this equation has the purely imaginary roots . A branch of periodic orbits arises through a Hopf bifurcation. Wright conjectured attraction to zero for every continuous real initial history of when . The proof of van den Berg and Jaquette (2018) completed the result for this range.