Permanence in a class of delay differential equations with mixed monotonicity

New results on global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies model with multiple pairs of time-varying delays

“…are established under the additional technical conditions on the delay terms [1]. Most recently, Győri et al [15] established the permanence in the following two constant-delay differential equation:…”

Positive periodic solutions for impulsive differential equations with infinite delay and applications to integro‐differential equations

“…The global dynamics of such equations have been the subject of a few recent studies, where questions of stability, persistence, permanence, and existence of periodic solutions were addressed. 4,19,29,31,33,34 Nevertheless, as far as the authors know, only the case of discrete delays has been considered.…”

“…However, DDEs with different delays in the same nonlinear term appear naturally in real‐world models, as shown in and references therein. The global dynamics of such equations have been the subject of a few recent studies, where questions of stability, persistence, permanence, and existence of periodic solutions were addressed . Nevertheless, as far as the authors know, only the case of discrete delays has been considered.…”

Global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies system involving multiple pairs of time-varying delays

“…Remark 4.1 It should be pointed out that the global asymptotic stability on the patch structure Nicholson's blowflies systems with nonlinear density-dependent mortality terms and multiple pairs of time-varying delays has not been touched in the previous literature. As in [16][17][18][19][20][21][22][23][24][25][26] and , the authors still do not make a point of the global asymptotic stability on the Nicholson's blowflies systems involving multiple pairs of time-varying delays, and we also mention that none of the consequences in [16][17][18][19][20][21][22][23][24][25][26] and can obtain the convergence of the zero equilibrium point in (4.1).…”

“…It should be mentioned that, up to now, the models (1.1), (1.2) and (1.3) relate to the global stability analysis of two or more delays are very few [1,[21][22][23][24]. For the special case of (1.2) with h j ≡ g j (j ∈ I), some delay-independent criteria ensuring the global asymptotic stability have been established in [25].…”