Abstract
In this paper, existence, uniqueness and global exponential stability of pseudo almost automorphic solutions for a class of recurrent neural networks with time-varying coefficients and mixed delays are established by employing the fixed point theorem and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.
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References
Chérif F (2014) Sufficient conditions for global stability and existence of almost automorphic solution of a class of RNNs. Differ Equ Dyn Syst 22(2):191–207
Cao J, Liang J, Lam J (2004) Exponential stability of high-order bidirectional associative memory neural networks with time delays. Phys D 199:425–436
Abbas S, Mahto L, Hafayed M, Alimi AM (2014) Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients. Neurocomputing 142(22):326–334
Ammar B, Chérif F, Alimi AM (2012) Existence and uniqueness of pseudo almost-periodic solution recurrent neural networks with time varying coefficient and mixed delays. IEEE Trans Neural Netw Learn Syst 23:109–118
Xiang H, Cao J (2009) Almost periodic solutions of recurrent neural networks with continuously distributed delays. Nonlinear Anal 71:6097–6108
Bai C (2009) Existence and stability of almost periodic solutions of hopfield neural networks with continuously distributed delays. Nonlinear Anal 71:5850–5859
Liang J, Zhang J, Xiao T-J (2008) Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl 340:1493–1499
Xiao T-J, Liang J, Zhang J (2008) Pseudo almost automorphic solutions to semilinear differential equations in banach spaces. Semigroup Forum 76(3):518524
Bochner S (1964) Continuous mappings of almost automorphic and almost periodic functions. Proc Natl Acad Sci USA 52:907910
Zhang CY (1994) Pseudo-almost-periodic solutions of some differential equations. J Math Anal Appl 151:6276
Zhang CY (1994) Integration of vector-valued pseudo-almost periodic functions. Proc Am Math Soc 121:167174
Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42:691–702
Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092
Abbas S (2011) Pseudo almost automorphic solutions of some nonlinear integro-differential equations. Comput Math Appl 62:2259–2272
Ezzinbi K, Fatajou S, N’guérékata GM (2009) Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces. Nonlinear Anal 70(4):1641–1647
Alia M, Ezzinbi K, Fatajou S (2009) Exponential dichotomy and pseudo-almost automorphy for partial neutral functional differential equations. Nonlinear Anal 71:2210–2226
Wang Yan, Li Yong (2011) Alternative theorems for pseudo almost automorphic problems. Taiwan J Math 15(1):59–74
Bai C (2008) Global stability of almost periodic solution of hopfield neural networks with neutral time-varying delays. Appl Math Comput 203:72–79
Liang J, Zhang J, Xiao T-J (2008) Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl 340:1493–1499
N’Guerekata GM (2005) Topics in almost automorphy. Springer, New York MR2107829 (2005h:34153)
Liang J, N’guérékata GM, Xiao T-J, Zhang J (2009) Some properties of pseudo-almost automorphic functions and applications to abstract differential equations. Nonlinear Anal 70:2731–2735
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Aouiti, C., M’hamdi, M.S. & Touati, A. Pseudo Almost Automorphic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays. Neural Process Lett 45, 121–140 (2017). https://doi.org/10.1007/s11063-016-9515-0
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DOI: https://doi.org/10.1007/s11063-016-9515-0