Research Article

Year 2024,
Volume: 14 Issue: 1, 39 - 50, 28.06.2024
### Abstract

### References

- [1] Hopfield, J.J., Neuron with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences of the United States of America, 81, 3088–92, 1984.
- [2] Chua, L. O., Yang,L., Cellular Neural Networks Theory, IEEE Transactions Circuits and Systems, 35, 10, 1257-1272, 1988.
- [3] Kato, S., Imai, M., On the existence of periodic and almost periodic solutions for nonlinear systems, Nonlinear Analysis, TMA 24, 1183-1192, 1995.
- [4] Kartsatos, A.G., Almost periodic solutions to nonlinear systems, Bollettino dell'Unione Matematica Italiana, 9, 10-15, 1974.
- [5] Seifert, G., Almost periodic solutions for a certain class of almost periodic systems, Proceedings of the American Mathematical Society, 84, 47-51, 1982.
- [6] Levitan, B.M., Zhikov, V.V., Almost Periodic Functions and Differential Equations, Cambridge University. Press, Cambridge, 1982.
- [7] Hall, J.K., Periodic and almost periodic solutions of functional-differential equations, Archive for Rational Mechanics and Analysis, 15, 289-304, 1964.
- [8] Li, Y.K., Lv, G., Meng, X.F., Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs, Journal of Inequalities and Applications, 1, 1–23, 2019.
- [9] Tian, Y.F., Wang, Z.S., Stochastic stability of Markovian neural networks with generally hybrid transition rates, IEEE Transactions on Neural Networks and Learning Systems, https://doi.org/10.1109/ TNNLS.2021.3084925.
- [10] Hou, Y.Y., Dai, L.H., Square-mean pseudo almost periodic solutions for quaternion-valued stochastic neural networks with time-varying delays, Mathematical Problems in Engineering 2021, 6679326, 2021.
- [11] Li, Y.K., Meng, X.F., Almost automorphic solutions in distribution sense of quaternion-valued stochastic recurrent neural networks with mixed time-varying delays, Neural Processing Letters, 51(4), 1353–1377, 2020.
- [12] Yang, T.Q., Xiong, Z.L., Yang, C.P., Analysis of exponential stability for neutral stochastic Cohen–Grossberg neural networks with mixed delays, Discrete Dynamics in Nature and Society 2019, 4813103, 2019.
- [13] Bohr, H., Zur Theorie der fast periodischen Funktionen I, Acta Mathematica, 45, 29–127, 1925.
- [14] Andres, J., Pennequin, D., On Stepanov almost-periodic oscillations and their discretizations, Journal of Difference Equations and Applications, 18(10), 1665–1682, 2012.
- [15] Andres, J., Pennequin, D., On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations, Proceedings of the American Mathematical Society, 140(8), 2825–2834, 2012.
- [16] Maqbul, Md., Bahuguna, D., Almost periodic solutions for Stepanov-almost periodic differential equations, Differential Equations and Dynamical Systems, 22, 251–264, 2014.
- [17] Henríquez, H.R., On Stepanov-almost periodic semigroups and cosine functions of operators, Journal of Mathematical Analysis and Applications, 146(2), 420–433, 1990.
- [18] Jiang, Q.D., Wang, Q.R., Almost periodic solutions for quaternion-valued neural networks with mixed delays on time scales, Neurocomputing, 439, 363–373, 2021.
- [19] Wang, T.Y., Zhu, Q.X., Cai, W., Mean-square exponential input-to-state stability of stochastic fuzzy recurrent neural networks with multi-proportional delays and distributed delays, Mathematical Problems in Engineering 2018, 6289019, 2018.
- [20] Doğan, Z., The investigation of stability properties of neutral type time delayed dynamic neural networks, Istanbul University-Cerrahpasa Institute of Graduate Studies Department of Computer Engineering, M.Sc. Thesis, 2019.
- [21] Xu, C., Mao, X., Existence and Exponential Stability of Anti-periodic Solutions for A Cellular Neural Networks with Impulsive Effects, Wseas Transactions on Signal Processing, 11, 140-149, 2015.
- [22] Wang, P., Li, B., Li, Y.K., Square-mean almost periodic solutions for impulsive stochastic shunting inhibitory cellular neural networks with delays, Neurocomputing, 167, 76–82, 2015.

Year 2024,
Volume: 14 Issue: 1, 39 - 50, 28.06.2024
### Abstract

### References

Bu çalışmada zaman gecikmeli bir ilişkisel sinir ağı modeli incelenmiştir. Bu denklemin neredeyse periyodik çözümlerinin varlığı araştırılmış, Lyapunov nokta teoremi ve diferansiyel eşitsizlik yardımıyla tekliği ve kararlılığı kanıtlanmıştır. Gerçek dünyada sinir ağının sinyal iletim süreci periyodik olarak değiştiğinden, birçok bilim adamı bu konuya ağırlık vermiş ve pratik olaylara daha uygun olması sebebi ile neredeyse periyodik fonksiyon çok önem kazanmıştır. Bulunan sonuçlar öncekilerden farklı ve onları tamamlayıcı niteliktedir.

- [1] Hopfield, J.J., Neuron with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences of the United States of America, 81, 3088–92, 1984.
- [2] Chua, L. O., Yang,L., Cellular Neural Networks Theory, IEEE Transactions Circuits and Systems, 35, 10, 1257-1272, 1988.
- [3] Kato, S., Imai, M., On the existence of periodic and almost periodic solutions for nonlinear systems, Nonlinear Analysis, TMA 24, 1183-1192, 1995.
- [4] Kartsatos, A.G., Almost periodic solutions to nonlinear systems, Bollettino dell'Unione Matematica Italiana, 9, 10-15, 1974.
- [5] Seifert, G., Almost periodic solutions for a certain class of almost periodic systems, Proceedings of the American Mathematical Society, 84, 47-51, 1982.
- [6] Levitan, B.M., Zhikov, V.V., Almost Periodic Functions and Differential Equations, Cambridge University. Press, Cambridge, 1982.
- [7] Hall, J.K., Periodic and almost periodic solutions of functional-differential equations, Archive for Rational Mechanics and Analysis, 15, 289-304, 1964.
- [8] Li, Y.K., Lv, G., Meng, X.F., Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs, Journal of Inequalities and Applications, 1, 1–23, 2019.
- [9] Tian, Y.F., Wang, Z.S., Stochastic stability of Markovian neural networks with generally hybrid transition rates, IEEE Transactions on Neural Networks and Learning Systems, https://doi.org/10.1109/ TNNLS.2021.3084925.
- [10] Hou, Y.Y., Dai, L.H., Square-mean pseudo almost periodic solutions for quaternion-valued stochastic neural networks with time-varying delays, Mathematical Problems in Engineering 2021, 6679326, 2021.
- [11] Li, Y.K., Meng, X.F., Almost automorphic solutions in distribution sense of quaternion-valued stochastic recurrent neural networks with mixed time-varying delays, Neural Processing Letters, 51(4), 1353–1377, 2020.
- [12] Yang, T.Q., Xiong, Z.L., Yang, C.P., Analysis of exponential stability for neutral stochastic Cohen–Grossberg neural networks with mixed delays, Discrete Dynamics in Nature and Society 2019, 4813103, 2019.
- [13] Bohr, H., Zur Theorie der fast periodischen Funktionen I, Acta Mathematica, 45, 29–127, 1925.
- [14] Andres, J., Pennequin, D., On Stepanov almost-periodic oscillations and their discretizations, Journal of Difference Equations and Applications, 18(10), 1665–1682, 2012.
- [15] Andres, J., Pennequin, D., On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations, Proceedings of the American Mathematical Society, 140(8), 2825–2834, 2012.
- [16] Maqbul, Md., Bahuguna, D., Almost periodic solutions for Stepanov-almost periodic differential equations, Differential Equations and Dynamical Systems, 22, 251–264, 2014.
- [17] Henríquez, H.R., On Stepanov-almost periodic semigroups and cosine functions of operators, Journal of Mathematical Analysis and Applications, 146(2), 420–433, 1990.
- [18] Jiang, Q.D., Wang, Q.R., Almost periodic solutions for quaternion-valued neural networks with mixed delays on time scales, Neurocomputing, 439, 363–373, 2021.
- [19] Wang, T.Y., Zhu, Q.X., Cai, W., Mean-square exponential input-to-state stability of stochastic fuzzy recurrent neural networks with multi-proportional delays and distributed delays, Mathematical Problems in Engineering 2018, 6289019, 2018.
- [20] Doğan, Z., The investigation of stability properties of neutral type time delayed dynamic neural networks, Istanbul University-Cerrahpasa Institute of Graduate Studies Department of Computer Engineering, M.Sc. Thesis, 2019.
- [21] Xu, C., Mao, X., Existence and Exponential Stability of Anti-periodic Solutions for A Cellular Neural Networks with Impulsive Effects, Wseas Transactions on Signal Processing, 11, 140-149, 2015.
- [22] Wang, P., Li, B., Li, Y.K., Square-mean almost periodic solutions for impulsive stochastic shunting inhibitory cellular neural networks with delays, Neurocomputing, 167, 76–82, 2015.

There are 22 citations in total.

Primary Language | English |
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Subjects | Partial Differential Equations |

Journal Section | Mathematics |

Authors | |

Publication Date | June 28, 2024 |

Submission Date | October 10, 2023 |

Acceptance Date | May 30, 2024 |

Published in Issue | Year 2024 Volume: 14 Issue: 1 |

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