Skip to main content
main-content

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Erschienen in: Neural Processing Letters 3/2022

31.01.2022

Existence and Finite-Time Stability of Besicovitch Almost Periodic Solutions of Fractional-Order Quaternion-Valued Neural Networks with Time-Varying Delays

verfasst von: Yongkun Li, Caifeng Ruan, Bing Li

Erschienen in: Neural Processing Letters | Ausgabe 3/2022

Einloggen, um Zugang zu erhalten
share
TEILEN

Abstract

Almost periodic oscillation is an important dynamics of neural networks. Therefore, there have been many studies on Bohr almost periodic, Stepanov almost periodic and Weyl almost periodic oscillations of neural networks. Besicovitch almost periodicity is a generalization of the above almost periodicity, but there is no research on Besicovitch almost periodicity of neural networks. In this paper, we study the Besicovitch almost periodic oscillation for a class of fractional-order quaternion-valued neural networks with time-varying delays. Firstly, we give a definition of almost periodic functions in the sense of Besicovitch, which we call \(B^{\mathcal {P}}\)-almost periodic functions. Then we introduce and prove some properties of these functions. Since the space composed of these functions is incomplete, we construct a suitable Banach space, and use the contraction fixed point theorem to obtain the existence and uniqueness of \(B^{\mathcal {P}}\)-almost periodic solutions of the considered neural network. Secondly, we use some inequality techniques to study the finite-time stability of the \(B^{\mathcal {P}}\)-almost periodic solution. Even when the system we consider degenerates into a real-valued system, our results are new. Finally, we use a numerical example to illustrate the feasibility and validity of our results.
Literatur
1.
Zurück zum Zitat Khan AT, Khan AR, Li S, Bakhsh S, Mehmood A, Zaib J (2021) Optimally configured gated recurrent unit using hyperband for the long-term forecasting of photovoltaic plant. Renew Energy Focus 39:49–58 CrossRef Khan AT, Khan AR, Li S, Bakhsh S, Mehmood A, Zaib J (2021) Optimally configured gated recurrent unit using hyperband for the long-term forecasting of photovoltaic plant. Renew Energy Focus 39:49–58 CrossRef
3.
Zurück zum Zitat Khan AT, Li S, Zhou X (2021) Trajectory optimization of 5-link biped robot using beetle antennae search. IEEE Trans Circ Syst II-Express Briefs 68:3276–3280 Khan AT, Li S, Zhou X (2021) Trajectory optimization of 5-link biped robot using beetle antennae search. IEEE Trans Circ Syst II-Express Briefs 68:3276–3280
5.
Zurück zum Zitat Li Z, Li S (2020) Saturated PI control for nonlinear system with provable convergence: an optimization perspective. IEEE Trans Circ Syst II: Express Briefs 68:742–746 Li Z, Li S (2020) Saturated PI control for nonlinear system with provable convergence: an optimization perspective. IEEE Trans Circ Syst II: Express Briefs 68:742–746
6.
Zurück zum Zitat Khan AH, Cao X, Li S, Katsikis VN, Liao L (2020) BAS-ADAM: an ADAM based approach to improve the performance of beetle antennae search optimizer. IEEE/CAA J. Auto. Sinica 7:461–471 CrossRef Khan AH, Cao X, Li S, Katsikis VN, Liao L (2020) BAS-ADAM: an ADAM based approach to improve the performance of beetle antennae search optimizer. IEEE/CAA J. Auto. Sinica 7:461–471 CrossRef
7.
Zurück zum Zitat Khan AH, Li S, Luo X (2019) Obstacle avoidance and tracking control of redundant robotic manipulator: an RNN-based metaheuristic approach. IEEE Trans. Ind. Inform. 16:4670–4680 CrossRef Khan AH, Li S, Luo X (2019) Obstacle avoidance and tracking control of redundant robotic manipulator: an RNN-based metaheuristic approach. IEEE Trans. Ind. Inform. 16:4670–4680 CrossRef
8.
Zurück zum Zitat Li Y, Qin J, Li B (2019) Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects. Math. Meth. Appl. Sci. 42(1):5–23 MathSciNetCrossRef Li Y, Qin J, Li B (2019) Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects. Math. Meth. Appl. Sci. 42(1):5–23 MathSciNetCrossRef
9.
Zurück zum Zitat Arbi A, Cao J (2017) Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Neural Process Lett 46(2):719–745 CrossRef Arbi A, Cao J (2017) Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Neural Process Lett 46(2):719–745 CrossRef
10.
Zurück zum Zitat Li Y, Xiang J (2020) Existence and global exponential stability of almost periodic solution for quaternion-valued high-order Hopfield neural networks with delays via a direct method. Math Meth Appl Sci 43(10):6165–6180 MathSciNetCrossRef Li Y, Xiang J (2020) Existence and global exponential stability of almost periodic solution for quaternion-valued high-order Hopfield neural networks with delays via a direct method. Math Meth Appl Sci 43(10):6165–6180 MathSciNetCrossRef
11.
Zurück zum Zitat Liu B, Tunc C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26(2):429–435 CrossRef Liu B, Tunc C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26(2):429–435 CrossRef
13.
Zurück zum Zitat Li Y, Zhao L (2017) Weighted pseudo-almost periodic functions on time scales with applications to cellular neural networks with discrete delays. Math. Meth. Appl. Sci. 40(6):1905–1921 MathSciNetCrossRef Li Y, Zhao L (2017) Weighted pseudo-almost periodic functions on time scales with applications to cellular neural networks with discrete delays. Math. Meth. Appl. Sci. 40(6):1905–1921 MathSciNetCrossRef
14.
Zurück zum Zitat Stamov G, Stamova I, Martynyuk A, Stamov T (2021) Almost periodic dynamics in a new class of impulsive reaction-diffusion neural networks with fractional-like derivatives. Chaos Solitons Fractals 143:110647 MathSciNetCrossRef Stamov G, Stamova I, Martynyuk A, Stamov T (2021) Almost periodic dynamics in a new class of impulsive reaction-diffusion neural networks with fractional-like derivatives. Chaos Solitons Fractals 143:110647 MathSciNetCrossRef
15.
Zurück zum Zitat Li Y, Huo N, Li B (2021) On \(\mu \)-pseudo almost periodic solutions for Clifford-valued neutral type neural networks with delays in the leakage term. IEEE Trans Neural Netw Learn Syst 32(3):1365–1374 MathSciNetCrossRef Li Y, Huo N, Li B (2021) On \(\mu \)-pseudo almost periodic solutions for Clifford-valued neutral type neural networks with delays in the leakage term. IEEE Trans Neural Netw Learn Syst 32(3):1365–1374 MathSciNetCrossRef
16.
Zurück zum Zitat Huang C, Yang H, Cao J (2021) Weighted pseudo almost periodicity of multi-proportional delayed shunting inhibitory cellular neural networks with D operator. Discrete Contin Dyn-S 14(4):1259–1272 MathSciNetMATH Huang C, Yang H, Cao J (2021) Weighted pseudo almost periodicity of multi-proportional delayed shunting inhibitory cellular neural networks with D operator. Discrete Contin Dyn-S 14(4):1259–1272 MathSciNetMATH
17.
Zurück zum Zitat Bohner M, Stamov GT, Stamova IM (2020) Almost periodic solutions of Cohen-Grossberg neural networks with time-varying delay and variable impulsive perturbations. Commun Nonlinear Sci Numer Simulat 80:104952 MathSciNetCrossRef Bohner M, Stamov GT, Stamova IM (2020) Almost periodic solutions of Cohen-Grossberg neural networks with time-varying delay and variable impulsive perturbations. Commun Nonlinear Sci Numer Simulat 80:104952 MathSciNetCrossRef
18.
Zurück zum Zitat Li B, Li Y (2019) Existence and global exponential stability of almost automorphic solution for Clifford-valued high-order Hopfield neural networks with leakage delays. Complexity 2019:6751806 Li B, Li Y (2019) Existence and global exponential stability of almost automorphic solution for Clifford-valued high-order Hopfield neural networks with leakage delays. Complexity 2019:6751806
19.
Zurück zum Zitat Li Y, Meng X (2020) Almost automorphic solutions for quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays. J Syst Sci Complex 33(1):100–121 MathSciNetCrossRef Li Y, Meng X (2020) Almost automorphic solutions for quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays. J Syst Sci Complex 33(1):100–121 MathSciNetCrossRef
20.
Zurück zum Zitat Kobayashi M (2017) Quaternionic Hopfield neural networks with twin-multistate activation function. Neurocomputing 267:304–310 CrossRef Kobayashi M (2017) Quaternionic Hopfield neural networks with twin-multistate activation function. Neurocomputing 267:304–310 CrossRef
21.
Zurück zum Zitat Liu Y, Zhang D, Lou J, Lu J, Cao J (2017) Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans Neural Netw Learn Syst 29(9):4201–4211 CrossRef Liu Y, Zhang D, Lou J, Lu J, Cao J (2017) Stability analysis of quaternion-valued neural networks: decomposition and direct approaches. IEEE Trans Neural Netw Learn Syst 29(9):4201–4211 CrossRef
22.
Zurück zum Zitat Liu Y, Zhang D, Lu J, Cao J (2016) Global \(\mu \)-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inform Sci 360:273–288 CrossRef Liu Y, Zhang D, Lu J, Cao J (2016) Global \(\mu \)-stability criteria for quaternion-valued neural networks with unbounded time-varying delays. Inform Sci 360:273–288 CrossRef
23.
Zurück zum Zitat Tu Z, Zhao Y, Ding N, Feng Y, Zhang W (2019) Stability analysis of quaternion-valued neural networks with both discrete and distributed delays. Appl Math Comput 343:342–353 MathSciNetMATH Tu Z, Zhao Y, Ding N, Feng Y, Zhang W (2019) Stability analysis of quaternion-valued neural networks with both discrete and distributed delays. Appl Math Comput 343:342–353 MathSciNetMATH
24.
Zurück zum Zitat Song Q, Chen Y, Zhao Z, Liu Y, Alsaadi FE (2021) Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 420:70–81 CrossRef Song Q, Chen Y, Zhao Z, Liu Y, Alsaadi FE (2021) Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties. Neurocomputing 420:70–81 CrossRef
25.
Zurück zum Zitat Song Q, Chen S, Zhao Z, Liu Y, Alsaadi FE (2021) Passive filter design for fractional-order quaternion-valued neural networks with neutral delays and external disturbance. Neural Netw 137:18–30 CrossRef Song Q, Chen S, Zhao Z, Liu Y, Alsaadi FE (2021) Passive filter design for fractional-order quaternion-valued neural networks with neutral delays and external disturbance. Neural Netw 137:18–30 CrossRef
26.
Zurück zum Zitat Udhayakumar K, Rakkiyappan R, Li X, Cao J (2021) Mutiple \(\psi \)-type stability of fractional-order quaternion-valued neural networks. Appl Math Comput 401:126092 MathSciNetMATH Udhayakumar K, Rakkiyappan R, Li X, Cao J (2021) Mutiple \(\psi \)-type stability of fractional-order quaternion-valued neural networks. Appl Math Comput 401:126092 MathSciNetMATH
27.
Zurück zum Zitat Xiao J, Cao J, Cheng J, Zhong S, Wen S (2020) Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inform Sci 526:221–244 MathSciNetCrossRef Xiao J, Cao J, Cheng J, Zhong S, Wen S (2020) Novel methods to finite-time Mittag-Leffler synchronization problem of fractional-order quaternion-valued neural networks. Inform Sci 526:221–244 MathSciNetCrossRef
28.
Zurück zum Zitat Li HL, Zhang L, Hu C, Jiang H, Cao J (2020) Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: direct quaternion approach. Appl Math Comput 373:125020 MathSciNetMATH Li HL, Zhang L, Hu C, Jiang H, Cao J (2020) Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: direct quaternion approach. Appl Math Comput 373:125020 MathSciNetMATH
29.
Zurück zum Zitat Yang S, Hu C, Yu J, Jiang H (2021) Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order. Chaos Solitons Fractals 147:110911 MathSciNetCrossRef Yang S, Hu C, Yu J, Jiang H (2021) Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order. Chaos Solitons Fractals 147:110911 MathSciNetCrossRef
30.
Zurück zum Zitat Huang C, Nie X, Zhao X, Song Q, Tu Z, Xiao M, Cao J (2019) Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 117:67–93 CrossRef Huang C, Nie X, Zhao X, Song Q, Tu Z, Xiao M, Cao J (2019) Novel bifurcation results for a delayed fractional-order quaternion-valued neural network. Neural Netw 117:67–93 CrossRef
31.
Zurück zum Zitat Li R, Cao J, Xue C, Manivannan R (2021) Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks. Appl Math Comput 395:125851 MathSciNetMATH Li R, Cao J, Xue C, Manivannan R (2021) Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks. Appl Math Comput 395:125851 MathSciNetMATH
32.
Zurück zum Zitat Wei H, Li R, Wu B (2021) Dynamic analysis of fractional-order quaternion-valued fuzzy memristive neural networks: vector ordering approach. Fuzzy Sets Syst 411:1–24 MathSciNetCrossRef Wei H, Li R, Wu B (2021) Dynamic analysis of fractional-order quaternion-valued fuzzy memristive neural networks: vector ordering approach. Fuzzy Sets Syst 411:1–24 MathSciNetCrossRef
33.
Zurück zum Zitat Li HL, Kao Y, Hu C, Jiang H, Jiang YL (2021) Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects. Chaos Solitons Fractals 143:110598 MathSciNetCrossRef Li HL, Kao Y, Hu C, Jiang H, Jiang YL (2021) Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects. Chaos Solitons Fractals 143:110598 MathSciNetCrossRef
34.
Zurück zum Zitat Li HL, Hu C, Zhang L, Jiang H, Cao J (2021) Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks. Appl Math Comput 409:126377 MathSciNetMATH Li HL, Hu C, Zhang L, Jiang H, Cao J (2021) Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks. Appl Math Comput 409:126377 MathSciNetMATH
35.
Zurück zum Zitat Corduneanu C (2009) Almost periodic oscillations and waves. Springer, New York CrossRef Corduneanu C (2009) Almost periodic oscillations and waves. Springer, New York CrossRef
36.
Zurück zum Zitat Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, Amsterdam MATH Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, Amsterdam MATH
37.
Zurück zum Zitat Ye H, Gao J, Ding Y (2007) A generalized Gronwall inequality and its application to a fractional differential equation. J Math Anal Appl 328:1075–1081 MathSciNetCrossRef Ye H, Gao J, Ding Y (2007) A generalized Gronwall inequality and its application to a fractional differential equation. J Math Anal Appl 328:1075–1081 MathSciNetCrossRef
38.
Zurück zum Zitat Li Y, Wang Y, Li B (2020) Existence and finite-time stability of a unique almost periodic positive solution for fractional-order Lasota-Wazewska red blood cell models. Int J Biomath 13(02):2050013 MathSciNetCrossRef Li Y, Wang Y, Li B (2020) Existence and finite-time stability of a unique almost periodic positive solution for fractional-order Lasota-Wazewska red blood cell models. Int J Biomath 13(02):2050013 MathSciNetCrossRef
Metadaten
Titel
Existence and Finite-Time Stability of Besicovitch Almost Periodic Solutions of Fractional-Order Quaternion-Valued Neural Networks with Time-Varying Delays
verfasst von
Yongkun Li
Caifeng Ruan
Bing Li
Publikationsdatum
31.01.2022
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 3/2022
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-021-10722-4

Weitere Artikel der Ausgabe 3/2022

Neural Processing Letters 3/2022 Zur Ausgabe