On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation

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Nicholson's blowflies differential equations revisited: Main results and open problems (2010, result): “In [13] the following general result was obtained: Theorem 2.”
DELAY DIFFERENTIAL EQUATIONS IN SINGLE SPECIES DYNAMICS (2006, background): “Equation (3.1) is now refereed to as the Nicholson’s blowflies equation, see Nisbet and Gurney (1982), Kulenović et al. (1992), So and Yu (1994), Smith (1995), Györi and Trofimchuk(2002), etc. 3.2.”
Nonmonotone travelling waves in a single species reaction–diffusion equation with delay (2005, background): “The next lemma can be considered as an extension of the linearized oscillation theorem from [15] to the second order delay differential equation εx(t)− x(t)− x(t) + g(x(t− h)) = 0, t ∈ R.”
Global dynamics of Nicholsonʼs blowflies equation revisited: Onset and termination of nonlinear oscillations (2013, background): “1) is globally asymptotically stable (with respect to nonnegative and nontrivial initial conditions) for any τ 0 provided that 1 < p/γ < e2 (see, for example, [12,16,28]).”