School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China.
College of Information Technology, Shanghai Ocean University, Shanghai 201306, China.
Neural Plast. 2021 Feb 2;2021:6692132. doi: 10.1155/2021/6692132. eCollection 2021.
In this paper, an analytical criterion is proposed to investigate the synchronization between two Hindmarsh-Rose neurons with linear and nonlinear coupling functions based on the Laplace transform method. Different from previous works, the synchronization error system is expressed in its integral form, which is more convenient to analyze. The synchronization problem of two HR coupled neurons is ultimately converted into the stability problem of roots to a nonlinear algebraic equation. Then, an analytical criterion for synchronization between the two HR neurons can be given by using the Routh-Hurwitz criterion. Numerical simulations show that the synchronization criterion derived in this paper is valid, regardless of the periodic spikes or burst-spike chaotic behavior of the two HR neurons. Furthermore, the analytical results have almost the same accuracy as the conditional Lyapunov method. In addition, the calculation quantities always are small no matter the linear and nonlinear coupling functions, which show that the approach presented in this paper is easy to be developed to study synchronization between a large number of HR neurons.
本文提出了一种分析准则，通过拉普拉斯变换方法，研究了具有线性和非线性耦合函数的两个 Hindmarsh-Rose 神经元之间的同步。与以往的工作不同，同步误差系统以积分形式表示，这更便于分析。两个 HR 耦合神经元的同步问题最终转化为非线性代数方程根的稳定性问题。然后，利用劳斯-赫尔维茨准则，可以给出两个 HR 神经元同步的分析准则。数值模拟表明，本文推导的同步准则是有效的，无论两个 HR 神经元的周期尖峰还是爆发尖峰混沌行为如何。此外，解析结果与条件李雅普诺夫方法几乎具有相同的精度。此外，无论线性和非线性耦合函数如何，计算量总是很小，这表明本文提出的方法很容易被发展为研究大量 HR 神经元之间的同步。
