Finite-Time Cluster Synchronization of Fractional-Order Complex-Valued Neural Networks Based on Memristor with Optimized Control Parameters
Abstract
:1. Introduction
- ①
- This paper studies the fractional-order CNNs with a time delay, where the network includes memristive elements and complex-valued states, resulting in a model that is not only more complex than those studied in [31,32] but also better suited for simulating real-world scenarios. Unlike the conventional decomposition approach [20,21,34], this study employs a non-decomposition method. Although the decomposition method simplifies theoretical analysis, it often falls short in practical applications. The non-decomposition approach, on the other hand, provides a more realistic representation of complex systems, aligning more closely with real-world dynamics.
- ②
- This paper focuses on FTCS, extending beyond conventional CS [35,36] or FTS [37], which has faster convergence time, and the synchronization time can be calculated in advance. To achieve FTCS, we design a simple controller based on the CVSF and derive synchronization criteria that provide a range of control parameters. The settling time for FTCS can be readily determined through the Mittag–Leffler function. While FTCS has been explored in previous studies [19,31,32], the networks investigated in those works differ significantly from the one considered here. Notably, this is the first study to address FTCS for FOCV-coupled neural networks with memristors using a non-decomposition method.
- ③
- An optimization model solved by PSO is proposed to select the most cost-effective control parameters. This optimization approach guides the selection of control parameters within a broad range that satisfies the synchronization conditions. Although previous studies [31,32] designed similar controllers, they only provided a range for the parameters without specifically focusing on actual control requirement.
Item | [19] | [32] | [20] | [31] | [34] | [21] | [37] | This Paper |
---|---|---|---|---|---|---|---|---|
Fractional-order | ✓ | ✓ | ✓ | ✓ | ✓ | |||
Complex-valued | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||
Memristor | ✓ | ✓ | ✓ | ✓ | ||||
FTS | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||
CS | ✓ | ✓ | ✓ | ✓ | ||||
Non-decomposition | ✓ | ✓ | ✓ | |||||
Parameter optimization | ✓ |
2. Preliminaries and Model Description
2.1. Preliminaries
- ①
- [32] .
- ②
- There exists such that , when , . , where .
2.2. Model Description
- ①
- ②
- ①
- ②
3. Main Results
4. Optimization of Control Parameters
4.1. The Optimization Model
4.2. An Algorithm with PSO
5. Simulation
5.1. Example 1
5.2. Example 2
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Method | Control | Parameters | J | ||
---|---|---|---|---|---|
Normal | 9.87 | 10.17 | 10.47 | 691.2507 | |
9.87 | 9.87 | 9.87 | |||
10.47 | 9.87 | 10.17 | |||
4.84 | 4.6 | ||||
Optimization | 10.6886 | 8.6932 | 573.7228 | ||
8.2978 | 9.6064 | 8.4519 | |||
0.0408 | 10.643 | 10.355 | |||
5.6879 | 3.7145 |
Method | J | |||||
---|---|---|---|---|---|---|
[31] | 9 | 8 | 5 | 5 | 7.6398 | |
Optimization | 13.8477 | 13.8515 | 2.5530 | 2.5525 | 7.5698 |
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Chang, Q.; Wang, R.; Yang, Y. Finite-Time Cluster Synchronization of Fractional-Order Complex-Valued Neural Networks Based on Memristor with Optimized Control Parameters. Fractal Fract. 2025, 9, 39. https://doi.org/10.3390/fractalfract9010039
Chang Q, Wang R, Yang Y. Finite-Time Cluster Synchronization of Fractional-Order Complex-Valued Neural Networks Based on Memristor with Optimized Control Parameters. Fractal and Fractional. 2025; 9(1):39. https://doi.org/10.3390/fractalfract9010039
Chicago/Turabian StyleChang, Qi, Rui Wang, and Yongqing Yang. 2025. "Finite-Time Cluster Synchronization of Fractional-Order Complex-Valued Neural Networks Based on Memristor with Optimized Control Parameters" Fractal and Fractional 9, no. 1: 39. https://doi.org/10.3390/fractalfract9010039
APA StyleChang, Q., Wang, R., & Yang, Y. (2025). Finite-Time Cluster Synchronization of Fractional-Order Complex-Valued Neural Networks Based on Memristor with Optimized Control Parameters. Fractal and Fractional, 9(1), 39. https://doi.org/10.3390/fractalfract9010039