Weighted pseudo almost automorphic solutions for neutral type fuzzy cellular neural networks with mixed delays and <i>D</i> operator in Clifford algebra

Aouiti, Chaouki; Dridi, Farah

doi:10.1080/00207721.2020.1777345

Cited by 31 publications

(17 citation statements)

References 48 publications

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“…However, the dynamical properties of Cliffordvalued NN models are typically more complex than those of real-valued and complexvalued NN models. As such, studies on Clifford-valued NN dynamics are still limited due to those utilizing the principle of non-commutativity of the product of Clifford numbers [33][34][35][36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the use of Banach fixed point theorem and Lyapunov-Krasovskii functional (LKF) technique for addressing the global asymptotic almost periodic synchronization issues for Clifford-valued cellular NN models was conducted in [38]. A study of the weighted pseudo almost automorphic solutions pertaining to neutral type fuzzy cellular NN models with mixed delays and D operator in Clifford algebra was presented in [40]. In [42], the authors investigated the existence of anti-periodic solutions corresponding to a class of Clifford-valued inertial Cohen-Grossberg NN models by constructing suitable LKFs.…”

Section: Introductionmentioning

confidence: 99%

“…Hence it is necessary to analyze the NN dynamics that incorporate either constant or time-varying delays. In this respect, NN models with various time delays have been extensively studied, and many significant results have been obtained [3,5,[11][12][13][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. On the other hand, due to noise, change in frequency, or switching phenomenon, the impulsive effects occur in real-world systems [47].…”

Section: Introductionmentioning

confidence: 99%

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Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

et al. 2021

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In this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the original n-dimensional Clifford-valued model into $2^{m}n$ 2 m n -dimensional real-valued models. Then we adopt the Lyapunov–Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

et al. 2021

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“…So it is important to analyze his dynamics behaviors. 8,[17][18][19][20][21][22][23] Rather than Lyapunov's classic asymptotic stability 6,[24][25][26][27] and exponential stability, 28 finite-time stability means that the system's solution trajectories converge the equilibrium point after a finite-time, and the finite-time is called the settling time or time convergence. [29][30][31][32] The finite-time stability is involved in many control problems, such as secure communication, 33 finite-time output feedback stabilization of the double integrator, 34 and the finite-time attitude tracking problem for a single spacecraft and multiple spacecraft.…”

Section: Introductionmentioning

confidence: 99%

“…The applications heavily depend on the dynamical behaviors of FNNs. So it is important to analyze his dynamics behaviors 8,17‐23 …”

Section: Introductionmentioning

confidence: 99%

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Aouiti

Jallouli

2021

Intl J Robust & Nonlinear

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This article addresses the problems of fixed-time stabilization for a class of quaternion fuzzy neural networks (QFNNs) with time-varying delay. The QFNNs are developed by dividing our system into four real-valued parts based on the Hamilton rule. Then, based on fixed-time stability theory, some inequality techniques, and selecting the appropriate controllers and Lyapunov function, a novel criterion guaranteeing the fixed-time stabilization and the finite-time stabilization of the addressed system is derived. Finally, three numerical examples are presented to show the effectiveness of our theoretical results. K E Y W O R D S finite-time stabilization, fixed-time stabilization, fuzzy neural networks, quaternion neural networks, time-varying delay

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B‐almost periodic solutions in finite‐dimensional distributions for octonion‐valued stochastic shunting inhibitory cellular neural networks

Huo,

2024

Math Methods in App Sciences

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In this paper, we consider a class of octonion‐valued stochastic shunting inhibitory cellular neural networks with delays. First, we give an estimate of the distance between two different moments of finite‐dimensional distributions of a stochastic process. Then, based on this and by using fixed point theorems and inequality techniques, we establish the existence and global exponential stability of Besicovitch almost periodic ( ‐almost periodic for short) solutions in finite‐dimensional distributions for this kind of networks. Our results are new even if the networks we consider in the paper are real‐valued ones. At the same time, the method proposed in this paper can be applied to study the existence of Besicovitch almost periodic solutions in finite‐dimensional distributions for other types of stochastic neural networks. Finally, an example is given to illustrate the effectiveness of our results.

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Weighted pseudo almost automorphic solutions for neutral type fuzzy cellular neural networks with mixed delays and D operator in Clifford algebra

Cited by 31 publications

References 48 publications

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

B‐almost periodic solutions in finite‐dimensional distributions for octonion‐valued stochastic shunting inhibitory cellular neural networks

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