Besicovitch almost automorphic stochastic processes in distribution and an application to Clifford-valued stochastic neural networks

Wang, Xiaohui; Huo, Nina

doi:10.1016/j.cnsns.2022.106488

Cited by 10 publications

(2 citation statements)

References 21 publications

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“…In addition, in the past few decades, the almost periodic dynamics [26][27][28][29][30][31][32][33] and the almost automorphic dynamics [34][35][36][37][38][39] of deterministic neural networks have been widely studied as one of their important dynamics. And there have been many studies on almost periodic dynamics of stochastic neural networks.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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“…As a high-dimensional neural network, the Clifford-valued neural network not only includes real-valued, complex-valued and quaternary-valued neural networks as its special cases, but also has greater advantages than low-dimensional neural networks in dealing with multidimensional data. In recent years, they have attracted more and more attention [2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks

Qi¹

2022

Mathematics

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The main purpose of this paper was to study the almost anti-periodic oscillation caused by external inputs and the global exponential synchronization of Clifford-valued recurrent neural networks with mixed delays. Since the space consists of almost anti-periodic functions has no vector space structure, firstly, we prove that the network under consideration possesses a unique bounded continuous solution by using the contraction fixed point theorem. Then, by using the inequality technique, it was proved that the unique bounded continuous solution is also an almost anti-periodic solution. Secondly, taking the neural network that was considered as the driving system, introducing the corresponding response system and designing the appropriate controller, some sufficient conditions for the global exponential synchronization of the driving-response system were obtained by employing the inequality technique. When the system we consider degenerated into a real-valued system, our results were considered new. Finally, the validity of the results was verified using a numerical example.

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Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions

Li,

Bai

2024

Math Methods in App Sciences

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In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite‐dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite‐dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion.

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Besicovitch almost automorphic stochastic processes in distribution and an application to Clifford-valued stochastic neural networks

Cited by 10 publications

References 21 publications

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

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

Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks

Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions

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