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

Abstract

This paper is concerned with a class of Nicholson's blowflies model involving nonlinear density-dependent mortality terms and multiple pairs of time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a delay-independent criterion on the global asymptotic stability of the addressed model, which improves and complements some existing ones. The effectiveness of the obtained result is illustrated by some numerical simulations.

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

“…We shall establish a delay-independent criterion to ensure the global asymptotic stability of (1.3) without τ ij ≡ σ ij (i ∈ Q, j ∈ I), which has not been investigated till now. Moreover, our consequences generalize and improve all known consequences in [25,26], and the error mentioned above has been corrected in Lemma 2.1.…”

“…Remark 3.1 Obviously, for the scalar equation (1.2), all the results of [25,26] are special cases in Theorem 3.1 because the adopted assumptions are weaker.…”

“…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).…”

“…The deficiency is that we can find some errors in the process of proving the main consequence in [25]. In fact, as pointed in [26], in lines 3-4 of page 856 in [25], letting t → η(ϕ)…”

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

“…In realistic engineering applications, humans continuously like to obtain synchronization in a finite convergence time, which is known as FTS. Moreover, time delays are inevitable in nearly all dynamical systems including neural network, chemical process, and nuclear reactors, which may lead to system oscillation, instability behaviors, and divergence because of the limited switching speed of amplifier circuits (see [44][45][46][47][48]). In recent decades, an increasing interest in the field of finite-time synchronization criterion of FONNs with time delays has attracted many scientific communities, which has given rise to some meaningful and significant outcomes (see [49][50][51]).…”