<p>This manuscript addresses the predefined synchronization in quaternion-valued neural networks (QVNNs) incorporating mixed time delays and leakage terms. Sufficient conditions for predefined-time synchronization of time-delayed QVNNs have been derived. The QVNNs have been decomposed into real-valued systems, and further synchronization criteria have been deliberated by constructing a suitable Lyapunov function. The novel aspect of the suggested scheme is that two new controllers are utilized to achieve predefined-time synchronization for quaternion-valued neural networks (QVNNs) with mixed and leakage time delays. Unlike traditional methods, this approach ensures synchronization within a specific time frame. The first controller uses the sign function, while the second employs exponential and Lyapunov functions, offering simplicity and fewer parameters. This method's flexibility and superior timing adjustment capabilities extend beyond traditional asymptotic finite-time and fixed-time synchronization, adding significant value to the literature by enhancing the practical utility of QVNNs in complex systems.</p>

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Predefined Synchronization of Mixed and Leakage-Delayed Quaternion-Valued Neural Network

  • Vijay K. Shukla,
  • Mahesh C. Joshi,
  • Prashant K. Mishra,
  • Yashar Mousavi,
  • Maryam Raeis Zadeh,
  • Afef Fekih

摘要

This manuscript addresses the predefined synchronization in quaternion-valued neural networks (QVNNs) incorporating mixed time delays and leakage terms. Sufficient conditions for predefined-time synchronization of time-delayed QVNNs have been derived. The QVNNs have been decomposed into real-valued systems, and further synchronization criteria have been deliberated by constructing a suitable Lyapunov function. The novel aspect of the suggested scheme is that two new controllers are utilized to achieve predefined-time synchronization for quaternion-valued neural networks (QVNNs) with mixed and leakage time delays. Unlike traditional methods, this approach ensures synchronization within a specific time frame. The first controller uses the sign function, while the second employs exponential and Lyapunov functions, offering simplicity and fewer parameters. This method's flexibility and superior timing adjustment capabilities extend beyond traditional asymptotic finite-time and fixed-time synchronization, adding significant value to the literature by enhancing the practical utility of QVNNs in complex systems.