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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 3
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Research Article

Stepanov stability for delayed Lotka–Volterra recurrent neural networks on time scales

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Pages 921-937 | Received 02 Feb 2021, Accepted 04 Aug 2021, Published online: 18 Aug 2021

References

  • Asai T, Fukai T, Tanaka S. A subthreshold MOS circuit for the Lotka–Volterra neural network producing the winner-share-all solution. Neur Netw. 1999;12:211–216.
  • Asai T, Ohtani M, Yonezu H. Analog integrated circuits for the Lotka-Volterra competitive neural networks. IEEE Trans Neur Netw. 1999;10:1222–1231.
  • Hu W, Zhu Q, Karimi HR. Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems. IEEE Trans Automatic Control. 2019;64(12):5207–5213.
  • Raflkov M, Tusset AM. Modeling and optimal control of predator-prey systems : applications in biological pest control. Dyn Contin Discrete Impuls Syst Ser B Appl Algorithm Sp Iss. 2005;2:658–662.
  • Su YH, Feng ZS. Homoclinic orbits and periodic solution for a class of Hamiltonian systems on time scales. J Math Anal Appl. 2014;411:37–62.
  • Zhu Q. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-Triggered feedback control. IEEE Trans Automatic Control. 2019;64(9):3764–3771.
  • Kuo TC, Huang YJ. Global stabilization of robot control with neural network and sliding mode. Eng Lett. 2008;16:56–60.
  • Melin P, Urias J, Solano D, et al. Voice recognition with neural networks, type-2 fuzzy logic and genetic algorithms. Eng Lett. 2006;13:108–116.
  • Liao Y. Almost periodicity in a harvesting Lotka–Volterra recurrent neural networks. Int J Math Comput Sci. 2013;7(5):00–00.
  • Zhang Y, Tan KK. Global convergence of Lotka–Volterra recurrent neural networks with delays. IEEE Trans Circuits Syst I Fundamental Theor Appl. 2005;52:2482–2489.
  • Amdouni M, Chérif F. The pseudo almost periodic solution of the new class of Lotka–Volterra recurrent neural networks with mixed delays. Chaos Solitons Fractals. 2018;113:79–88.
  • Hilger S. Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten [PhD]. University Würzburg; 1988.
  • Aticia FM, Bilesa DC, Lebedinsky A. An application of time scales to economics. Math Comput Model. 2006;43:718–726.
  • Li Y, Zhao L. Weighted pseudo almost periodic functions on time scales with applications to cellular neural networks with discrete delays. Math Meth Appl Sci. 2016;40:1905–1921.
  • Shen S, Li B, Li Y. Anti-periodic dynamics of quaternion-valued fuzzy cellular neural networks with time-varying delays on time scales. Discrete Dyn Nat Soc. 2018;2018(3–4):1–14.Article ID 5290786, 14 pages Available from: https://doi.org/10.1155/2018/5290786.
  • Zhou H, Zhou ZF, Jiang W. Almost periodic solution for neutral type BAM neural networks with distributed leakage delays on time scales. Neurocomputing. 2015;157:223–230.
  • Bochner S. Continuous mappings of almost automorphic and almost periodic functions. Proc Natl Acad Sci. 1964;52(4):907–910.
  • Lizama C, Mesquit JG. Almost automorphic solutions of dynamic equations on time scales. J Funct Anal. 2013;265:2267–2311.
  • Tang CH, Li H. Stepanov-like pseudo almost periodic functions on time scales and applications to dynamic equations with delay. Math. 2018;16:826–841.
  • Zitane M. A generalization of weighted Stepanov-like pseudo-almost automorphic space. New Zealand J Math. 2018;48:129–155.
  • Es-saiydy M, Zitane M, Zarhouni M. Stepanov-like pseudo almost automorphy on time scales: new developments and applications. Submitted for publication.
  • Es-Saiydy M, Zitane M. Stepanov-like pseudo almost automorphic dynamics of QVRNNS with mixed delays on time scales via a direct method. Asia Pac J Math. 2020;7(32):7–32. doi: 10.28924/APJM/7-32.
  • Bohner M, Hari Rao VS, Sanyal S. Global stability of complex-valued neural networks on time scales. Differ Equ Dyn Syst. 2011;19:3–11.
  • Cabada A, Vivero DR. Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral; application to the calculus of Δ-antiderivatives. Math Comput Model. 2006;43:194–207.
  • Es-saiydy M, Zitane M. Weighted Stepanov-like pseudo almost periodicity on time scales and applications. Differ Equ Dyn Syst. 2020; Available from: https://doi.org/10.1007/s12591-020-00543-7.
  • Lou XY, Cui BT. Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays. Math Anal Appl. 2007;330:144–158.
  • Liu Y, Liu B, Ling S. The almost periodic solution of Lotka–Volterra recurrent neural networks with delays. Neurocomputing. 2011;74(6):1062–1068.
  • Es-saiydy M, Zitane M. Dynamic behavior of a class of delayed Lotka–Volterra recurrent neural networks on time scales. Russian mathematics. (To appear).

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