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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Dynamical Analysis of the Hindmarsh–Rose Neuron With Time Delays
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Dynamical Analysis of the Hindmarsh–Rose Neuron With Time Delays

机译：具有时间延迟的Hindmarsh-Rose神经元动力学分析

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摘要

This brief is mainly concerned with a series of dynamical analyses of the Hindmarsh–Rose (HR) neuron with state-dependent time delays. The dynamical analyses focus on stability, Hopf bifurcation, as well as chaos and chaos control. Through the stability and bifurcation analysis, we determine that increasing the external current causes the excitable HR neuron to exhibit periodic or chaotic bursting/spiking behaviors and emit subcritical Hopf bifurcation. Furthermore, by choosing a fixed external current and varying the time delay, the stability of the HR neuron is affected. We analyze the chaotic behaviors of the HR neuron under a fixed external current through time series, bifurcation diagram, Lyapunov exponents, and Lyapunov dimension. We also analyze the synchronization of the chaotic time-delayed HR neuron through nonlinear control. Based on an appropriate Lyapunov–Krasovskii functional with triple integral terms, a nonlinear feedback control scheme is designed to achieve synchronization between the uncontrolled and controlled models. The proposed synchronization criteria are derived in terms of linear matrix inequalities to achieve the global asymptotical stability of the considered error model under the designed control scheme. Finally, numerical simulations pertaining to stability, Hopf bifurcation, periodic, chaotic, and synchronized models are provided to demonstrate the effectiveness of the derived theoretical results.
机译：本摘要主要涉及对具有状态依赖时间延迟的Hindmarsh-Rose（HR）神经元进行的一系列动力学分析。动力学分析的重点是稳定性，Hopf分叉以及混沌和混沌控制。通过稳定性和分叉分析，我们确定外部电流的增加会导致兴奋性HR神经元表现出周期性或混沌的突发/尖峰行为，并发出亚临界Hopf分支。此外，通过选择固定的外部电流并更改时间延迟，会影响HR神经元的稳定性。我们通过时间序列，分叉图，李雅普诺夫指数和李雅普诺夫维数分析了在固定外部电流下HR神经元的混沌行为。我们还通过非线性控制分析了混沌时延HR神经元的同步。基于具有三重积分项的适当Lyapunov–Krasovskii泛函，设计了一种非线性反馈控制方案，以实现不受控制的模型与受控模型之间的同步。根据线性矩阵不等式推导提出的同步准则，以在设计的控制方案下实现所考虑误差模型的全局渐近稳定性。最后，提供了与稳定性，Hopf分叉，周期，混沌和同步模型有关的数值模拟，以证明导出的理论结果的有效性。

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