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<p>Synchronization issues are key research topics in the theory of stochastic neural networks. This paper is committed to investigating the fixed and preassigned-time projective (FITP and PATP for short) lag synchronization of stochastic quaternion-valued BAM neural networks (SQV-BAMNNs) with generalized delays. A generalized form of time delays, encompassing both discrete and proportional delays, is introduced. Subsequently, without employing the quaternion separation method, two discontinuous control strategies based on 1-norm and 2-norm are designed to achieve FITP/PATP lag synchronization of SQV-BAMNNs. Next, by constructing different Lyapunov functions and leveraging the quaternion-valued Itô’s differential formula, novel criteria for FITP/PATP lag synchronization of SQV-BAMNNs are derived. At last, the rationality of theoretical analysis is further validated by numerical simulation.</p>

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Projective lag synchronization of full quaternion-valued stochastic BAM neural networks with generalized delays

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Siyu Han,
  • Zhiming Li,
  • Cheng Hu,
  • Shenglong Chen

摘要

Synchronization issues are key research topics in the theory of stochastic neural networks. This paper is committed to investigating the fixed and preassigned-time projective (FITP and PATP for short) lag synchronization of stochastic quaternion-valued BAM neural networks (SQV-BAMNNs) with generalized delays. A generalized form of time delays, encompassing both discrete and proportional delays, is introduced. Subsequently, without employing the quaternion separation method, two discontinuous control strategies based on 1-norm and 2-norm are designed to achieve FITP/PATP lag synchronization of SQV-BAMNNs. Next, by constructing different Lyapunov functions and leveraging the quaternion-valued Itô’s differential formula, novel criteria for FITP/PATP lag synchronization of SQV-BAMNNs are derived. At last, the rationality of theoretical analysis is further validated by numerical simulation.