| Citation: |
Yanxia Hu, Xiaofang Meng, Zhouhong Li, Jinde Cao. QUASI-SYNCHRONIZATION OF COMPLEX-VALUED NEUTRAL-TYPE INERTIAL NEURAL NETWORKS WITH PROPORTIONAL DELAYS[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1276-1297. doi: 10.11948/20250262
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QUASI-SYNCHRONIZATION OF COMPLEX-VALUED NEUTRAL-TYPE INERTIAL NEURAL NETWORKS WITH PROPORTIONAL DELAYS
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Abstract
This article explores the quasi-synchronization of complex-valued neutral-type inertial neural networks with proportional delays. By constructing appropriate Lyapunov functions and utilizing inequality techniques, sufficient conditions for the quasi-synchronization of the error system are derived. The entire analysis employs a non-reduced order approach and a non-separation method, it is directly concerned with the original system. A control law is designed, and it is proven that, under certain conditions, the error between the response system and the driving system can be bounded, thereby achieving quasi-synchronization. Finally, the effectiveness of these findings is thoroughly validated through numerical examples, and the research results are applied to the processes of image encryption and decryption. In terms of innovation, this paper focuses on models with parameter mismatch. It can provide theoretical references for the research on parameter-mismatched systems, and its analysis methods can also be applied to parameter-matched systems. At the same time, it provides more efficient analysis tools for complex-valued neural networks and further advances the theoretical foundations of quasi-synchronization control.
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References
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Yanxia Hu, Xiaofang Meng, Zhouhong Li, Jinde Cao. QUASI-SYNCHRONIZATION OF COMPLEX-VALUED NEUTRAL-TYPE INERTIAL NEURAL NETWORKS WITH PROPORTIONAL DELAYS[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1276-1297. doi: 10.11948/20250262
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Figure 1.
Trajectory diagram of the state variables
$ x_{i}^{R}(t) $ $ x_{i}^{I}(t) $ -
Figure 2.
Trajectory diagram of the first-order state variables
$ \dot{x}_{i}^{R}(t) $ $ \dot{x}_{i}^{I}(t) $ -
Figure 3.
Trajectory diagram of the state variables
$ y_{i}^{R}(t) $ $ y_{i}^{I}(t) $ -
Figure 4.
Trajectory diagram of the first-order state variables
$ \dot{y}_{i}^{R}(t) $ $ \dot{y}_{i}^{I}(t) $ -
Figure 5.
Trajectory diagram of the state variables
$ z_{i}^{R}(t) $ $ z_{i}^{I}(t) $ -
Figure 6.
Original image, encrypted image, decrypted image.
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Figure 7.
The histograms corresponding to the original image and the encrypted image.
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Figure 8.
The correlation between the original image and the encrypted image in the horizontal, vertical, and diagonal directions.