In this paper, authors present a memristor-based fractional order system of tri-diagonal bidirectional associative memory neural networks (TdBAMNNs) incorporating leakage and communication delays. The existence and uniqueness theorem is established for the memristor-based fractional-order TdBAMNNs system. Analysis of Hopf bifurcation anti-control is conducted using various feedback controllers by exploring single-parameter and double-parameter approaches. A study of the stability switching curves is undertaken to determine the direction of stability transitions in the system. The theoretical results and graphical illustrations are validated through numerical simulations to exhibit their feasibility. Comparative analysis of the system’s dynamical behavior under different controllers is performed. This paper comprehensively explores the proposed memristor-based system, proving its theoretical underpinnings, and analyzing stability through bifurcation control strategies and comparative assessments under different control scenarios.

中文翻译：

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各种控制器下基于忆阻器的分数级延迟三对角线双向关联记忆神经网络的 hopf 分叉控制


在本文中，作者提出了一种基于忆阻器的三对角双向关联记忆神经网络 （TdBAMNN） 分数阶系统，其中包含泄漏和通信延迟。为基于忆阻器的分数阶 TdBAMNNs 系统建立了存在性和唯一性定理。通过探索单参数和双参数方法，使用各种反馈控制器对 Hopf 分叉反控制进行分析。对稳定性切换曲线进行了研究，以确定系统中稳定性转变的方向。通过数值模拟验证了理论结果和图形说明，以证明其可行性。对系统在不同控制器下的动态行为进行了比较分析。本文全面探讨了所提出的基于忆阻器的系统，证明了其理论基础，并通过分岔控制策略和不同控制场景下的比较评估分析了稳定性。