Abstract
In this article, we investigated a class of genetic regulatory networks (GRNs) with time-varying delays and Stepanov-like weighted pseudo-almost automorphic coefficients. By Banach fixed point theorem, we firstly established the existence results of the weighted pseudo-almost automorphic solutions for the proposed GRNs. Secondly, by using suitable Lyapunov functional and mathematical analysis skills, new criteria are derived for ensuring the global exponential stability of the solutions. Finally, a numerical example and remarks are provided to substantiate the efficiency of obtained results. The derived results of this article are new and complement many earlier works and the ideas of this work can be applied to investigate other similar systems.
Similar content being viewed by others
References
Alimi AM, Aouiti C, Chérif F, Dridi F, M’hamdi MS (2018) Dynamics and oscillations of generalized high-order Hopfield neural networks with mixed delays. Neurocomputing 321:274–295
Blot J, Mophou GM, N’Guérékata GM, Pennequin D (2009) Weighted pseudo almost automorphic functions and applications to abstract differential equations. Nonlinear Anal Theory Methods Appl 71(3–4):903–909
Bochner S (1962) A new approach to almost periodicity. Proc Natl Acad Sci USA 48(12):2039
Boukli Hacene N, Ezzinbi K (2011) Weighted pseudo-almost automorphic solutions for some partial functional differential equations. Nonlinear Anal Real World Appl 12(1):562–570
Berdnikov V, Lokhin V (2019) Synthesis of guaranteed stability regions of a nonstationary nonlinear system with a fuzzy controller. Civ Eng J 5(1):107–116
Casarino V (2000) Almost automorphic groups and semigroups. Rend Accad Naz Sci XL Mem Mat Appl 24(5):219–235
Chang YK, Zheng S (2016) Weighted pseudo almost automorphic solutions to functional differential equations with infinite delay. Electron J Differ Equ 2016(286):1–19
Diagana T (2013) Almost automorphic type and almost periodic type functions in abstract spaces. Springer, New York
Duan L, Di F, Wang Z (2019) Existence and global exponential stability of almost periodic solutions of genetic regulatory networks with time-varying delays. J Exp Theor Artif Intell 32:453–463
Dhama S, Abbas S (2020) Existence and stability of weighted pseudo almost automorphic solution of dynamic equation on time scales with weighted Stepanov-like \(S^p\)-pseudo almost automorphic coefficients. Qual Theory Dyn Syst. https://doi.org/10.1007/s12346-020-00385-2
Khaled ZS, Ali RSA, Hasan MF (2017) Modeling the completion time of public school building projects using neural networks. Civil Eng J 3(12):1266–1277
Memarian T, Shahbazi Y (2017) Integrated metaheuristic differential evolution optimization algorithm and pseudo static analysis of concrete gravity dam. Civ Eng J 3(8):617–625
N’Guérékata GM (2007) Topics in almost automorphy. Springer, Berlin
Ratnavelu K, Kalpana M, Balasubramaniam P (2018) Stability analysis of fuzzy genetic regulatory networks with various time delays. Bull Malay Math Sci Soc 41(1):491–505
Ren F, Cao J (2008) Asymptotic and robust stability of genetic regulatory networks with time-varying delays. Neurocomputing 71:834–842
Wang L, Dong Y, Xie D, Cao J (2020) Global Dissipativity for Stochastic Genetic Regulatory Networks With Time-Delays. IEEE Access 8:34880–34887
Xiao TJ, Liang J, Zhang J (2008) Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces. In: Semigroup forum. Springer, Berlin, pp 518–524
Xia Z, Fan M (2012) Weighted Stepanov-like pseudo almost automorphy and applications. Nonlinear Anal Theory Methods Appl 75(4):2378–2397
Zhang R, Chang YK, N’Guérékata GM (2013) Weighted pseudo almost automorphic mild solutions to semilinear integral equations with \(S^p\)weighted pseudo almost automorphic coefficients. Discrete Contin Dyn Syst A 33:5525–5537
Zhang J, Ma L, Liu Y (2016) Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects. Neurocomputing 216:657–665
Zhao L, Li Y, Li B (2018) Weighted pseudo-almost automorphic solutions of high-order Hopfield neural networks with neutral distributed delays. Neural Comput Appl 29(7):513–527
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aouiti, C., Dridi, F. Study of genetic regulatory networks with Stepanov-like pseudo-weighted almost automorphic coefficients. Neural Comput & Applic 33, 10175–10187 (2021). https://doi.org/10.1007/s00521-021-05780-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-021-05780-7