$$S^{p}$$-Almost Periodic Solutions of Clifford-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays

Shen, Shiping

doi:10.1007/s11063-019-10176-9

Cited by 34 publications

(28 citation statements)

References 50 publications

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“…< CςM ψϕ 0 e ξ (t, t 0 ), which contradicts (8), and so (7) holds. Letting ς → 1, we conclude that (5) holds.…”

Section: Theorem 41 Let (S 1 )-(S 3 )mentioning

confidence: 85%

“…Therefore the fuzzy cellular neural networks are widely used in the fields such as pattern recognition, computer science, artificial intelligence, optimal control, equation solving, robotics, military science, and so on. Because the application of neural networks in these fields is related to their long-term behaviors and the time delay is inevitable in real neural networks, the dynamics of fuzzy cellular neural networks with various time delays has been extensively studied [3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

Shen

2020

Adv Differ Equ

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At present, the research on discrete-time Clifford-valued neural networks is rarely reported. However, the discrete-time neural networks are an important part of the neural network theory. Because the time scale theory can unify the study of discrete- and continuous-time problems, it is not necessary to separately study continuous- and discrete-time systems. Therefore, to simultaneously study the pseudo almost periodic oscillation and synchronization of continuous- and discrete-time Clifford-valued neural networks, in this paper, we consider a class of Clifford-valued fuzzy cellular neural networks on time scales. Based on the theory of calculus on time scales and the contraction fixed point theorem, we first establish the existence of pseudo almost periodic solutions of neural networks. Then, under the condition that the considered network has pseudo almost periodic solutions, by designing a novel state-feedback controller and using reduction to absurdity, we obtain that the drive-response structure of Clifford-valued fuzzy cellular neural networks on time scales with pseudo almost periodic coefficients can realize the global exponential synchronization. Finally, we give a numerical example to illustrate the feasibility of our results.

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“…< CςM ψϕ 0 e ξ (t, t 0 ), which contradicts (8), and so (7) holds. Letting ς → 1, we conclude that (5) holds.…”

Section: Theorem 41 Let (S 1 )-(S 3 )mentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

Shen

2020

Adv Differ Equ

Self Cite

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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%

“…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%

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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“…Since Clifford-valued neural networks have the ability to employ multi-state activation functions to process multi-level information, they have become actively researched in recent years. Recently, the dynamic behaviors of Clifford-valued neural networks were investigated in [9,[26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of Clifford-valued dynamic systems with D-operator on time scales

et al. 2021

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In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are taken into account. As an extension of the real-valued neural network, the Clifford-valued neural network, which includes a familiar complex-valued neural network and a quaternion-valued neural network as special cases, has been an active research field recently. By utilizing this novel method, which incorporates the differential inequality techniques and the fixed point theorem and time-scale theory of computation, we derive a few sufficient conditions to ensure the existence, uniqueness, and exponential stability of the pseudo almost periodic () solution of the considered model. The results in this paper are new, even if time scale $\mathbb{T}=\mathbb{R}$ T = R or $\mathbb{T}=\mathbb{Z}$ T = Z , and complementary to the previously existing works. Furthermore, an example and its numerical simulations are included to demonstrate the validity and advantage of the obtained results.

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$$S^{p}$$-Almost Periodic Solutions of Clifford-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays

Cited by 34 publications

References 50 publications

Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

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

Asymptotic behavior of Clifford-valued dynamic systems with D-operator on time scales

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