Novel stability criteria on nonlinear density-dependent mortality Nicholson’s blowflies systems in asymptotically almost periodic environments

Abstract

In this paper, we consider nonlinear density-dependent mortality Nicholson's blowflies system involving patch structures and asymptotically almost periodic environments. By developing an approach based on differential inequality techniques coupled with the Lyapunov function method, some criteria are demonstrated to guarantee the global attractivity of the addressed systems. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the obtain results.

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).…”

“…which in the classical case τ ij ≡ σ ij (i ∈ Q, j ∈ I) has been widely studied in the literature of the past [16][17][18][19][20]. In the ith patch, a ii (t)x i (t) b ii (t)+x i (t) labels the death rate of the the current population level x i (t); β ij (t)x i (tτ ij (t))e -γ ij (t)x i (t-σ ij (t)) designates the time-dependent birth function which requires maturation delays τ ij (t) and incubation delays σ ij (t), and gets the maximum reproduction rate 1 γ ij (t) ; for i, j ∈ Q and j = i, the weight function…”

Stability of antiperiodic recurrent neural networks with multiproportional delays

“…The influence of time delay on the dynamic behavior of neural network systems has become a fundamental problem and attracted much attention in the research of natural science and engineering technology . Nowadays, several types of delays such as constant delay, bounded time‐varying delay, distributed delay, and proportional delay have been successful used to model various practical problems in fields of population biology, electrodynamics, astrophysics, control theory, and web routing decision .…”

Mittag‐Leffler stability and adaptive impulsive synchronization of fractional order neural networks in quaternion field

“…We know that the next state of a system depends not only upon its current state but also upon its historical information. In addition to the classical delay differential equation modeling, fractional calculus is also a pretty effective tool to describe the nonlocal and weakly singular kernel . As usual, there are two advantages in models of fractional order: One is allowing more degree of freedom in the models, and the other is describing memory properties in the models.…”