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<p>This article investigates fixed-time lag synchronization (FTLS) for a class of inertial complex-valued recurrent neural networks (ICVRNNs) with mixed time-dependent delays, where one is a discrete delay, and the other is a distributed delay, respectively. Since the chosen model is inertial, i.e., second-order, it has been converted into first-order using the reduced-order technique. Additionally, the considered model is complex-valued, and it has been decomposed into two equivalent real components, a real component and imaginary component. Here, two different types of feedback controllers with dynamic exponential terms, different controller parameters multiplied by the signum function, and error signals are designed to achieve FTLS. Based on Lyapunov stability principles and certain inequality techniques and conditions, it is demonstrated that ICVRNNs can achieve FTLS with the aid of controllers. The value of control parameters is completely determined when the models can complete the required synchronization. Lastly, this article presents two suitable numerical examples to verify the authenticity of the theoretical aspects.</p>

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Lag-Synchronization at a Fixed-Time of an Inertial Recurrent Neural Network with Mixed-Time Varying Delays in the Complex Domain.

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Arpita Charan,
  • Rajeev,
  • Ankit Kumar,
  • Jinde Cao

摘要

This article investigates fixed-time lag synchronization (FTLS) for a class of inertial complex-valued recurrent neural networks (ICVRNNs) with mixed time-dependent delays, where one is a discrete delay, and the other is a distributed delay, respectively. Since the chosen model is inertial, i.e., second-order, it has been converted into first-order using the reduced-order technique. Additionally, the considered model is complex-valued, and it has been decomposed into two equivalent real components, a real component and imaginary component. Here, two different types of feedback controllers with dynamic exponential terms, different controller parameters multiplied by the signum function, and error signals are designed to achieve FTLS. Based on Lyapunov stability principles and certain inequality techniques and conditions, it is demonstrated that ICVRNNs can achieve FTLS with the aid of controllers. The value of control parameters is completely determined when the models can complete the required synchronization. Lastly, this article presents two suitable numerical examples to verify the authenticity of the theoretical aspects.