Stability Analysis of Fractional‐Order Bidirectional Associative Memory Neural Networks with Mixed Time‐Varying Delays

Abstract

This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

New results on finite‐time stability of fractional‐order Cohen–Grossberg neural networks with time delays

“…Remark In the existing works, there have been many works [36‐38,51] on the FTS of fractional‐order neural networks. The FTS criteria are obtained by virtue of integer‐order Gronwall inequality.…”

“…If max{||𝜓||, ||ℶ ′ (0)||} ≤ 𝛿 and the inequality (4) are satisfied, then from the inequality (13) Remark 1. In the existing works, there have been many works [36][37][38]51] on the FTS of fractional-order neural networks. The FTS criteria are obtained by virtue of integer-order Gronwall inequality.…”

“…Recently, many methods have been developed to handle the delay term in the systems. In previous studies [36][37][38], the supremum technique and the integer-order Gronwall inequality with nonlinear term in the integral were applied to handle the term delay in FODNNs. In previous studies [27,39], the Hölder inequality was used to transform the delay terms in FODNNs to the non-delay terms.…”

Artificial neural networks: a practical review of applications involving fractional calculus

“…Caputo derivative [38] Hopfield FANN [16,63] Memristive FANN [15] Nonidentical FANN [64] Quaternion-valued FANN [65] Quaternion-valued memristive FANN [41,66] Recurrent FANN FDE [67] Laplace transform method Backpropagation ANN Riemann-Liouville derivative FDE [68] Laplace transform method ANN Grünwald-Letnikov FANN FDE [44] Variational iteration method Feed-forward ANN Riemann-Liouville and Caputo derivative [73] Delayed cellular ANN [74][75][76] Delayed FANN [77,78] Delayed BAM FANN [79][80][81] Delayed complex-valued FANN Delayed FDE [82] Adams-Bashforth-Moulton method Delayed Fuzzy Cellular FANN Caputo derivative [83][84][85][86][87][88][89] Delayed Hopfield FANN [90][91][92] Delayed memristive FANN [93] Delayed memristive quaternion-valued FANN [94] Delayed quaternion-valued FANN Delayed FDE [95] Adams-Bashforth-Moulton method Delayed FANN Riemann-Liouville derivative [96] Delayed competitive FANN Hopfield FANN [74,[100][101][102] Delayed FANN [103][104][105] Delayed BAM FANN…”

Finite-Time Stability Criteria for a Class of High-Order Fractional Cohen–Grossberg Neural Networks with Delay

“…In order to more accurately model the dynamics of neurons, various fractional-order neural networks (FONNs) have been generated based on the integration of the fractional calculus and neural networks. In the recent decades, the research on FONNs has undergone a prosperous development, and there have been numerous works (see [10,[15][16][17][18][19][20] and the references therein). As we all know, the successful applications of FONNs are closely associated to the dynamics of networks, among which stability has been an active topic.…”