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<p>This paper proposes a dimensionally consistent passivity framework for complex-valued memristive neural networks (CVMNNs) with proportional delays (PDs), rectifying the complex-real mismatch in prior definitions. By constructing novel Lyapunov-Krasovskii functionals (LKFs), we establish easily verifiable sufficient conditions in linear matrix inequality (LMI) form for passivity. For global polynomial stabilization (GPS), an adaptive controller preserving original PD characteristics is designed, avoiding auxiliary variable substitutions in existing methods. Algebraic GPS criteria are derived via non-separation LKF analysis, eliminating dimensional expansion artifacts. Validations include: (i) passivity/GPS simulations under chaotic dynamics, (ii) application to secure image encryption achieving 7.9975 information entropy and near-zero pixel correlation (0.00254).</p>

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Novel passivity analysis and global polynomial stabilization of complex-valued memristive neural networks with proportional delays for secure image encryption

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Yongkang Zhang,
  • Liqun Zhou

摘要

This paper proposes a dimensionally consistent passivity framework for complex-valued memristive neural networks (CVMNNs) with proportional delays (PDs), rectifying the complex-real mismatch in prior definitions. By constructing novel Lyapunov-Krasovskii functionals (LKFs), we establish easily verifiable sufficient conditions in linear matrix inequality (LMI) form for passivity. For global polynomial stabilization (GPS), an adaptive controller preserving original PD characteristics is designed, avoiding auxiliary variable substitutions in existing methods. Algebraic GPS criteria are derived via non-separation LKF analysis, eliminating dimensional expansion artifacts. Validations include: (i) passivity/GPS simulations under chaotic dynamics, (ii) application to secure image encryption achieving 7.9975 information entropy and near-zero pixel correlation (0.00254).