<p>This paper studies the multiparty synchronization (MPS) issue of coupled memristive neural networks (CMNNs) with fixed-time and explores its application in image encryption. With construction of suitable leader-followers network model and the design of two discontinuous control strategies, named as delay-dependent control and delay-independent control, the nodes in networks can realize the MPS with small control cost, and the required time is controllable and computable. Based on the Lyapunov stability theory, several synchronization criteria and sufficient conditions are derived. Moreover, the upper boundary of settling time for CMNNs is relative smaller, which is more in line with the simulations. Then, one MPS-based image encryption algorithm is put forward, such that the encryption can be accomplished within a predictable and bounded time, and the security robustness against key-sensitivity attacks is enhanced as well. Several simulation examples are finally supplied to verify the validity of the proposed approach. The simulation outcomes indicate that under the proposed control strategy, the nodes in networks can achieve the synchronization within 1.76s, with the Normalized Cross-Correlation Coefficient(NPCR) of the image encryption reaching <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11547_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$99.62\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>99.62</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> and the Unified Average Changing Intensity(UACI) being <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11547_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$29.22\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>29.22</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

Fixed-time multiparty synchronization of coupled memristive neural networks via discontinuous control and its application to image encryption

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发表日期：

2025年7月11日

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Lili Zhou,
Changxin Wu,
Fei Tan,
Yukun Li

摘要

This paper studies the multiparty synchronization (MPS) issue of coupled memristive neural networks (CMNNs) with fixed-time and explores its application in image encryption. With construction of suitable leader-followers network model and the design of two discontinuous control strategies, named as delay-dependent control and delay-independent control, the nodes in networks can realize the MPS with small control cost, and the required time is controllable and computable. Based on the Lyapunov stability theory, several synchronization criteria and sufficient conditions are derived. Moreover, the upper boundary of settling time for CMNNs is relative smaller, which is more in line with the simulations. Then, one MPS-based image encryption algorithm is put forward, such that the encryption can be accomplished within a predictable and bounded time, and the security robustness against key-sensitivity attacks is enhanced as well. Several simulation examples are finally supplied to verify the validity of the proposed approach. The simulation outcomes indicate that under the proposed control strategy, the nodes in networks can achieve the synchronization within 1.76s, with the Normalized Cross-Correlation Coefficient(NPCR) of the image encryption reaching $99.62\%$ $99.62 %$ and the Unified Average Changing Intensity(UACI) being $29.22\%$ $29.22 %$ .