Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India.
Department of Mathematics, Sidho-Kanho-Birsha University, Purulia 723104, West Bengal, India.
Chaos. 2022 Aug;32(8):083121. doi: 10.1063/5.0084606.
In this article, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modeled using the nearest neighbor coupling theory, in which the diffusion part measures the spatial distribution of coupling topology. We derive analytically the conditions for traveling wave profiles that allow the construction of the shape of traveling nerve impulses. The analytical and numerical results are used to explore the nature of propagating pulses. The symmetric or asymmetric nature of traveling pulses is characterized, and the wave velocity is derived as a function of system parameters. Moreover, we present our results for an extended excitable medium by considering a slow-fast biophysical model with a homogeneous, diffusive coupling that can exhibit various traveling pulses. The appearance of series of pulses is an interesting phenomenon from biophysical and dynamical perspective. Varying the perturbation and coupling parameters, we observe the propagation of activities with various amplitude modulations and transition phases of different wave profiles that affect the speed of pulses in certain parameter regimes. We observe different types of traveling pulses, such as envelope solitons and multi-bump solutions, and show how system parameters and coupling play a major role in the formation of different traveling pulses. Finally, we obtain the conditions for stable and unstable plane waves.
本文报告了在同质的、扩散耦合的、激发的快慢动力学神经元网络中传播脉冲的产生和传播。使用最近邻耦合理论对空间扩展系统进行建模，其中扩散部分衡量了耦合拓扑的空间分布。我们从理论上推导出了允许构建传播神经脉冲形状的行波轮廓的条件。分析和数值结果用于探索传播脉冲的性质。对行波的对称或非对称性质进行了特征化，并推导出波速作为系统参数的函数。此外，我们通过考虑具有均匀扩散耦合的快慢生物物理模型，为扩展的激发介质呈现了各种传播脉冲。从生物物理和动力学的角度来看，脉冲序列的出现是一个有趣的现象。通过改变扰动和耦合参数，我们观察到具有不同幅度调制和不同波型相移的活动的传播，这些活动在某些参数范围内影响脉冲的速度。我们观察到不同类型的传播脉冲，如包络孤子和多峰解，并展示了系统参数和耦合如何在形成不同的传播脉冲中发挥主要作用。最后，我们得到了稳定和不稳定平面波的条件。
