On Stepanov weighted pseudo almost automorphic solutions of neural networks
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Abstract
In this paper, we investigate some sufficient conditions to guarantee the existence and uniqueness of Stepanov-like weighted pseudo almost periodic solutions of cellular neural networks on Clifford algebra for non-automomous cellular neural networks with multi-proportional delays. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.
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References
[1] S. Abbas, V.Kavitha and R.Murugesu, Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations, Proc. Indian Acad. Sci. 125 (2015), 323–351. Google Scholar
[2] C. Aouiti, F. Dridi, Q. Hui and E. Moulay, (μ, ν)-pseudo almost automorphic solutions of neutral type Clifford-valued high-order Hopfield neural networks with D operator, Neurocomputing. 53 (2021), 799–828. Google Scholar
[3] C. Aouiti, M. M’hamdi and F. Cherif, The existence and the stability of weighted pseudo almost periodic solution of high-order Hopfield neural network, Springer International Publishing Switzerland. (2016), 478–485. Google Scholar
[4] C. Aouiti, M. M’hamdi and A.Touati, Pseudo almost automorphic solutions of recurrent neural networks with time-varying coefficients and mixed delays, Neural Process Lett. 45 (2017), 121– 140. Google Scholar
[5] F. Cherif, M. Abdelaziz, Steaponov-like pseudo almost periodic solutions of quaternion-valued for fuzzy recurrent neural networks with mixed delays, Neural Process Lett. 51 (2020), 2211–2243. Google Scholar
[6] T. Diagana, Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, Springer International Publishing Switzerland. 2013. Google Scholar
[7] A.M. Fink, Almost periodic differential equations, Lecture notes in mathematics, Springer Berlin, 377 (1974). Google Scholar
[8] N. Hou, B. Li and Y. Li, Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays, Int.J.Appl.Math.Comput.Sci. 30 (2020), 83–98. Google Scholar
[9] A. N. Kolmogorov, On the representation of continuous functions of many variables by supetposition of continuous functions one variable andaddition, Doklady Akademmi Nauk SSSE, 114 (1957), 953–956. Google Scholar
[10] H. M. Lee, Stepanov almost periodic solutions of Clifford-valued neural works , J. Chungcheong Math. Soc. 35 (2022) no.1, 39–52. Google Scholar
[11] J. Liang, J. Zhang and T. Xiao, Composition of pseudo almost automorphic and asymptotically almost automorphic functions, Journal of Mathematical Analysis and Applications, 340 (2008), 1493–1499. Google Scholar
[12] B. Liu, Global exponential convergence of non-autonomous cellular neural networks with multi- proportional delays, Neurocomputing. 191 (2016), 352–355. Google Scholar
[13] B. Li, Y. Li, Existence and Global Exponential Stability of Pseudo Almost Periodic Solution for Clifford- Valued Neutral High-Order Hopfield Neural Networks With Leakage Delays, IEEE. 7 (2019), 121–140. Google Scholar
[14] M. Maqbul, Stepanov-almost periodic solutions of non-autonomous neutral functional differential equations with functional delay, Mediterr. J. Math. 179 (2018), no.15. Google Scholar
[15] S. Shen, Y. Li, Sp-Almost periodic solutions of Clifford-valued fuzzy cellular neural networks with time-varing delays, Neural Processing Lett. 51 (2020), 1749–1769. Google Scholar