Scholarlink

<p>The diverse firing characteristics of the excitable dynamical models are spontaneous organized responses often observed in networks. The adaptive exponential integrate-and-fire (AdEx) model has been widely used to study functional properties in neuronal networks and information processing. The dynamics of piecewise-linear approximation to the AdEx model is explored to enhance mathematical and computational efficiency and accuracy. Analytical calculations and numerical schemes are implemented to solve coupled nonlinear diffusive dynamical equations for traveling wave solutions. More specifically, we explore the diversity among the types of wave we encounter. We determined the approximate solutions using our proposed method and derived the solutions from variations in the diffusion parameters. The traveling front and pulses are explicitly specified and analyzed to validate our analytical scheme. This study contributes to understanding the role of self-diffusion and single cross-diffusion in piecewise linear AdEx models, providing insights into the mechanisms underlying action potential generation. We analyze the effects of different types of diffusion on the model’s behavior, including the generation of wave propagation, wave speed, and shape. The findings have implications for modeling neuronal activity, particularly in replicating complex behavior in neuronal computation.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A piecewise-linear adaptive exponential integrate-and-fire neuron model with emerging traveling waves using analytical scheme

  • 期刊论文

  • 发表日期：

    2025年5月22日

查看全文
  • Chinmay Chakraborty,
  • Naresh Saha,
  • M. A. Aziz-Alaoui,
  • Argha Mondal,
  • Chris G. Antonopoulos,
  • Evgeny P. Zemskov

摘要

The diverse firing characteristics of the excitable dynamical models are spontaneous organized responses often observed in networks. The adaptive exponential integrate-and-fire (AdEx) model has been widely used to study functional properties in neuronal networks and information processing. The dynamics of piecewise-linear approximation to the AdEx model is explored to enhance mathematical and computational efficiency and accuracy. Analytical calculations and numerical schemes are implemented to solve coupled nonlinear diffusive dynamical equations for traveling wave solutions. More specifically, we explore the diversity among the types of wave we encounter. We determined the approximate solutions using our proposed method and derived the solutions from variations in the diffusion parameters. The traveling front and pulses are explicitly specified and analyzed to validate our analytical scheme. This study contributes to understanding the role of self-diffusion and single cross-diffusion in piecewise linear AdEx models, providing insights into the mechanisms underlying action potential generation. We analyze the effects of different types of diffusion on the model’s behavior, including the generation of wave propagation, wave speed, and shape. The findings have implications for modeling neuronal activity, particularly in replicating complex behavior in neuronal computation.