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<p>This paper focuses an in-depth investigation into the fixed-time synchronization (FIXTS) and preassigned-time synchronization (PRETS) problems of delayed spatiotemporal memristive fuzzy neural networks (DSMFNNs). Firstly, to address the issues of parameter redundancy and insufficient information transmission efficiency in traditional control strategies, a novel simple power-law control strategy with only a single free parameter is innovatively designed, which significantly reduces the complexity of parameter tuning. Meanwhile, breaking through the limitation of the traditional quadratic norm framework, a flexible Lyapunov function based on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-norm is constructed to provide more general theoretical support for the derivation of synchronization criteria. Subsequently, combined with the fixed-time stability theorem and inequality scaling techniques, concise criteria for achieving FIXTS of DSMFNNs are strictly derived. Furthermore, by constructing an improved power-law control scheme, the PRETS problem of such networks is thoroughly explored. Finally, the feasibility of the proposed control design and the effectiveness of the theoretical criteria are fully verified through the simulation results and analysis of numerical simulations.</p>

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New results on fixed/preassigned-time synchronization of spatiotemporal memristive fuzzy neural networks with time delays

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Yinjie Qian,
  • Xuyan Jiang,
  • Yuanhua Qiao

摘要

This paper focuses an in-depth investigation into the fixed-time synchronization (FIXTS) and preassigned-time synchronization (PRETS) problems of delayed spatiotemporal memristive fuzzy neural networks (DSMFNNs). Firstly, to address the issues of parameter redundancy and insufficient information transmission efficiency in traditional control strategies, a novel simple power-law control strategy with only a single free parameter is innovatively designed, which significantly reduces the complexity of parameter tuning. Meanwhile, breaking through the limitation of the traditional quadratic norm framework, a flexible Lyapunov function based on the \(p\) -norm is constructed to provide more general theoretical support for the derivation of synchronization criteria. Subsequently, combined with the fixed-time stability theorem and inequality scaling techniques, concise criteria for achieving FIXTS of DSMFNNs are strictly derived. Furthermore, by constructing an improved power-law control scheme, the PRETS problem of such networks is thoroughly explored. Finally, the feasibility of the proposed control design and the effectiveness of the theoretical criteria are fully verified through the simulation results and analysis of numerical simulations.