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<p>This paper investigates fixed-time projective synchronization (FIXPS) and predefined-time projective synchronization (PREPS) in a class of discontinuous delayed BAM neural networks. First, a novel and widely applicable predefined-time stability criterion is established, which significantly enhances the flexibility in presetting the synchronization time. Second, based on the theory of differential inclusions and inequality techniques, we propose several effective controllers. Furthermore, novel criteria are derived to ensure that the drive-response systems achieve FIXPS and PREPS, respectively. The key distinction from previous studies is that these results are rigorously constructed using a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-norm Lyapunov function. This approach exhibits broader applicability and stronger practical value compared with analogous results derived from the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1\)</EquationSource> </InlineEquation>-norm. Finally, rigorous numerical simulations are provided to verify the effectiveness and applicability of the proposed schemes.</p>

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Fixed-/predefined-time projective synchronization of discontinuous BAM neural networks with time delays

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Yinjie Qian,
  • Yuanhua Qiao

摘要

This paper investigates fixed-time projective synchronization (FIXPS) and predefined-time projective synchronization (PREPS) in a class of discontinuous delayed BAM neural networks. First, a novel and widely applicable predefined-time stability criterion is established, which significantly enhances the flexibility in presetting the synchronization time. Second, based on the theory of differential inclusions and inequality techniques, we propose several effective controllers. Furthermore, novel criteria are derived to ensure that the drive-response systems achieve FIXPS and PREPS, respectively. The key distinction from previous studies is that these results are rigorously constructed using a \(p\) -norm Lyapunov function. This approach exhibits broader applicability and stronger practical value compared with analogous results derived from the \(1\) -norm. Finally, rigorous numerical simulations are provided to verify the effectiveness and applicability of the proposed schemes.