1/2] - 1 for sufficiently large h, hence Rouche's theorem
(where we compare [R.
2](t) has the unique zero t = 1/2 in the disk [absolute value of t] < r, it follows from Rouche's theorem
that h(t) also has the unique zero in the disk [absolute value of t] < r.
By Rouche's Theorem, the transcendental equation (i) has roots with positive real parts if and only if it has purely imaginary roots.
By Rouche's Theorem, the real parts of all the eigenvalues of the characteristic equation corresponding to equilibrium point B are negative for all delay [tau] > 0.
Using general form of Rouche's Theorem
we conclude that r(z) - r([beta]) has only a simple zero at [beta].
An application of the principle of the argument or Rouche's Theorem
shows such a root to exist with all other roots of modulus greater than 3/4.