Novel stability criteria on a patch structure Nicholson’s blowflies model with multiple pairs of time-varying delays

Global population dynamics of a single species structured with distinctive time-varying maturation and self-limitation delays

“…Y. Xu et al [21] and X. Long [14] also established the global stability on the zero equilibrium point for classical Nicholson's blowflies models involving distinctive delays. It should be mentioned that the stability on the positive equilibrium point for the addressed models in [6,21,14] has not been touched.…”

“…As [6,21,14], in [16,11], the authors still were unable to derive any global convergence for the positive equilibrium point of (1.2). Theorem 3.1 complements the aforementioned works and this seems to be the first time that such a result is derived for this type of Nichlson's blowflies equation.…”

On periodic solutions of a discrete Nicholson’s dual system with density-dependent mortality and harvesting terms

“…For most of biological systems, population dynamics, e.g., gene regulatory systems, are needed to be globally stable [ 1 – 4 ]. In addition, the global asymptotical stability of the positive equilibrium of a dynamical system is one of the research foci in theoretical studies of both continuous and discrete bio-mathematical models [ 5 – 11 ].…”

“…Long investigated a patch structure Nicholson’s blowflies model involving multiple pairs of different time-varying delays for , [ 11 ]. The author established three novel criteria to check the global convergence, generalized exponential convergence, and asymptotical stability on the zero equilibrium point of the addressed model, without assuming the uniform positiveness of the death rate and the boundedness of coefficients, respectively (see [ 11 ]).…”

“…Long investigated a patch structure Nicholson’s blowflies model involving multiple pairs of different time-varying delays for , [ 11 ]. The author established three novel criteria to check the global convergence, generalized exponential convergence, and asymptotical stability on the zero equilibrium point of the addressed model, without assuming the uniform positiveness of the death rate and the boundedness of coefficients, respectively (see [ 11 ]). Zhang et al established the existence and global exponential stability of positive almost periodic solutions for Nicholson’s blowflies systems involving patch structure and nonlinear density-dependent mortality terms by applying differential inequality techniques and the fluctuation lemma which guarantees the existence of positive asymptotically almost periodic solutions for the addressed system [ 12 ].…”