We present an extension of the well-known 3/2-stability criterion by Yorke for two term functional differential equations. We prove the exact nature of the obtained stability region which coincides with the Yorke result in the special case when the decay term is absent. Moreover, we reveal some interesting links existing between the Yorke conditions, Halanay inequalities and differential equations with maxima, all of them essentially involving the maximum functionals.
In this note, we present a monostable delayed reaction-diffusion equation with the unimodal birth function which admits only non-monotone wavefronts. Moreover, these fronts are either eventually monotone (in particular, such is the minimal wave) or slowly oscillating. Hence, for the Mackey-Glass type diffusive equations, we answer affirmatively the question about the existence of non-monotone non-oscillating wavefronts. As it was recently established by Hasik et al. and Ducrot et al., the same question has a negative answer for the KPP-Fisher equation with a single delay.
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