Global exponential stability of delayed inertial competitive neural networks

Abstract

In this paper, the exponential stability for a class of delayed competitive neural networks is studied. By applying the inequality technique and non-reduced-order approach, some novel and useful criteria of global exponential stability for the addressed network model are established. Moreover, a numerical example is presented to show the feasibility and effectiveness of the theoretical 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…”

Periodicity on Neutral-Type Inertial Neural Networks Incorporating Multiple Delays

“…During the past thirty decades, by utilizing the reduced-order transformation, numerous studies have been conducted on the stability and synchronization of system (1) and its generalizations, such as [3][4][5][6][7][8][9][10][11]. However, the reduced-order method will affect the dimensions of systems, thereby increasing a large amount of calculation, which will make it difficult to achieve in practice.…”

“…(2) Under certain assumptions, by exploiting the non-reduced order approach, one new sufficient stability criterion to guarantee the existence and stability of the T-periodic solutions on system (3) is gotten for the first time; (3) NTINNs here are second-order and involve multiple neutral delays, which are different from the traditional NNs [33][34][35][36][37][38][39][40] or INNs [3][4][5][6][7][8][9][11][12][13][14][15][17][18][19][20][21][30][31][32]. Compared with the results on exponential stability for the neutral-type neural networks (NTNNs) [26,29,39,41] and INNs [13,14,18,19], we give the exponential stability of the T-periodic solution for the NTINNs.…”

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

“…On account of this, fractional order calculus was introduced into artificial neural network in past few decades, namely, fractional order neural networks (FNNs), which can describe the neurodynamics of human brain more effectively and accurately in view of the hereditary and memory possessed by fractional calculus. Hence, the consideration of its dynamic behaviors like synchronization and stability plays a significant role in both theoretical and application perspectives, see for instance previous studies . Bao and Cao gave sufficient conditions to ascertain projective synchronization conditions for real‐valued FNNs by means of fractional order differential inequality.…”