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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stability Analysis and Almost Periodic Solutions for Quaternion-Valued Cellular Neural Networks with Leakage Term on Time Scales

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 757--774 | DOI:10.5890/DNC.2023.12.004

Mahammad Khuddush$^{1}$, K. Rajendra Prasad$^2$

$^1$ Department of Mathematics, Dr. Lankapalli Bullayya College of Engineering, Resapuvanipalem,

Viskhapatnam, 530013, Andhra Pradesh, India

$^2$ Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam,

530003, India

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Abstract

In this paper, we consider a quaternion-valued cellular neural networks with time varying delays in leakage term on time scales. We derive sufficient conditions for the existence, uniqueness and global exponential stability of almost periodic solutions by using contraction mapping principle and exponential dichotomy of linear dynamic equations. Finally, a numerical example is provided to illustrate the feasibility of our results.

Acknowledgments

\bibitem{levitan}Levitan, B.M. and Zhikov, V.V. (1982), \textit{Almost Periodic Functions and Differential Equations}, Cambridge University Press, Cambridge/New York.

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