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

Abstract

The finite‐time stability (FTS) of fractional‐order delayed Cohen–Grossberg neural networks (FODCGNNs) with the order ℘ ∈ (1, 2) is investigated in this study. Based on the fractional‐order delayed Gronwall inequality (FODGI), a new sufficient condition to guarantee the FTS of FODCGNNs is established, which reduces the conservation of the existing criterion. Finally, one numerical example is exhibited to illustrate the effectiveness and less conservativeness of the obtained results.

Stability analysis for fractional‐order neural networks with time‐varying delay

“…That is, the delay is usually time-varying. Fractional-order neural networks with time-varying delay have gradually emerged and developed into a research hotspot [15][16][17].…”

Stability Analysis of Fractional Difference Equations with Delay

“…The parameter values a = f ′ (0) for the logistic and cubic maps are λ and (1 − β), respectively. We plot the stability region of the system (16) in the b − a plane using the curves (17), (18) and the parametric curve (19) for different values of α and τ for logistic and cubic maps. Figures 5(a), (b), (d), and (e) show the stability region for τ = 1 and α = 0.5, 0.75 for logistic and cubic maps.…”

“…Certain inequalities have been derived for fractional order delay difference equations [1,14,46,17,18]. However, detailed bifurcation analysis of possible routes to instability has not been carried out to the best of our knowledge.…”

New results on finite‐time guaranteed cost control of uncertain polytopic fractional‐order systems with time‐varying delays

“…Later, this concept was developed for FOs and many important results have been addressed for many kinds of FOs by various approaches. [19][20][21][22][23][24][25][26][27][28] By improved fractional-order Gronwall integral inequality with time delays, Du and Lu have solved the problem for some kinds of fractional-order neural networks model such as Hopfield neural networks, 19 and bidirectional associative memory neural networks, 20 fuzzy cellular neural networks, 21 and Cohen-Grossberg memristive neural networks. 22 Feng et al 23 studied the problem of FTS and stabilization of singular fractional-order switched systems without time delays by using multiple Lyapunov functions and LMIs techniques.…”

“…By employing suitable Lyapunov–Krasovskii functional combined with Wirtinger‐based inequality, a set of sufficient conditions ensuring the finite‐time extended dissipative performance for the considered fuzzy systems were presented in terms of LMIs in this work. Later, this concept was developed for FOs and many important results have been addressed for many kinds of FOs by various approaches 19‐28 . By improved fractional‐order Gronwall integral inequality with time delays, Du and Lu have solved the problem for some kinds of fractional‐order neural networks model such as Hopfield neural networks, 19 and bidirectional associative memory neural networks, 20 fuzzy cellular neural networks, 21 and Cohen‐Grossberg memristive neural networks 22 .…”