Refined stability analysis of complex-valued neural networks with time-varying delays

N. Mohamed Thoiyab; Mostafa Fazly; R. Vadivel; Nallappan Gunasekaran; N. Mohamed Thoiyab; Mostafa Fazly; R. Vadivel; Nallappan Gunasekaran

doi:10.3934/nhm.2026017

Networks and Heterogeneous Media

2026, Volume 21, Issue 2: 368-386. doi: 10.3934/nhm.2026017

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Research article

Refined stability analysis of complex-valued neural networks with time-varying delays

1.
Department of Mathematics, Jamal Mohamed College, Affiliated to Bharathidasan University, Tiruchirappalli 620020, Tamilnadu, India
2.
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, United States of America
3.
Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, Thailand
4.
Department of Natural Sciences, Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, China

Received: 20 November 2025 Revised: 06 March 2026 Accepted: 10 March 2026 Published: 20 March 2026
93D05, 34D23, 34D08, 68T07

In this paper, we investigate the global asymptotic stability of complex-valued neural networks (CVNNs) subject to time-varying delays and parameter uncertainties. We establish novel stability conditions that guarantee both the existence and uniqueness of equilibrium states, as well as the global convergence of the network trajectories. By constructing a suitable Lyapunov-Krasovskii functional, the approach inherently accounts for the stability of CVNNs subject to time-varying delays. Finally, numerical examples are presented to verify the theoretical findings, illustrating both the effectiveness and the practical applicability of the proposed approach.
- Complex-valued neural networks,
- Lyapunov-Krasovskii functional,
- Global asymptotic stability,
- Time-varying delays
Citation: N. Mohamed Thoiyab, Mostafa Fazly, R. Vadivel, Nallappan Gunasekaran. Refined stability analysis of complex-valued neural networks with time-varying delays[J]. Networks and Heterogeneous Media, 2026, 21(2): 368-386. doi: 10.3934/nhm.2026017

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Abstract

In this paper, we investigate the global asymptotic stability of complex-valued neural networks (CVNNs) subject to time-varying delays and parameter uncertainties. We establish novel stability conditions that guarantee both the existence and uniqueness of equilibrium states, as well as the global convergence of the network trajectories. By constructing a suitable Lyapunov-Krasovskii functional, the approach inherently accounts for the stability of CVNNs subject to time-varying delays. Finally, numerical examples are presented to verify the theoretical findings, illustrating both the effectiveness and the practical applicability of the proposed approach.

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