Recently, a class of two-dimensional integrate and fire models has been used to faithfully model spiking neurons. This class includes the Izhikevich model, the adaptive exponential integrate and fire model, and the quartic integrate and fire model. The bifurcation types for the individual neurons have been thoroughly analyzed by Touboul (SIAM J Appl Math 68(4):1045-1079, 2008). However, when the models are coupled together to form networks, the networks can display bifurcations that an uncoupled oscillator cannot. For example, the networks can transition from firing with a constant rate to burst firing. This paper introduces a technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations. The reduction uses population density methods and a quasi-steady state approximation to arrive at the mean field system. Reduced models are derived for networks with different topologies and different model neurons with biologically derived parameters. The mean field equations are able to qualitatively and quantitatively describe the bifurcations that the full networks display. Extensions and higher order approximations are discussed.

Wilten Nicola

Sue Ann Campbell

Journal of computational neuroscience

计算神经科学杂志为适合神经科学计算和实验工作之间接口的论文提供了一个论坛。 《计算神经科学杂志》发表完整的原创论文、快速通讯和评论文章，描述与大脑和神经系统计算相关的理论和实验工作。特别鼓励结合理论和实验工作的论文。主要的理论论文应该处理与生物神经系统明显相关的问题。实验论文应该对神经系统的计算功能有影响，并且可以使用包括解剖学、电生理学、生物物理学、成像和分子生物学在内的各种方法中的任何一种来报告结果。研究神经系统病理生理机制的论文，或报告计算神经科学研究人员感兴趣的新技术的论文，包括神经数据分析方法的进展，从而深入了解神经系统的功能，也受到欢迎（在这种情况下，方法论论文应包括新方法的应用，举例说明它产生的见解）。预计从认知到细胞的所有分析水平都将在计算神经科学杂志上发表。

The Journal of Computational Neuroscience provides a platform for the exchange of ideas between computational and experimental neuroscience. This journal publishes original research articles, brief communications, and review papers that describe theoretical and experimental work related to the computation of the brain and nervous system. Papers that integrate theory and experiment are particularly encouraged. Major theoretical papers should address issues that are clearly relevant to biological neural systems, while experimental papers should impact the computational functions of the nervous system and may report results using a variety of methods, including anatomy, electrophysiology, biophysics, imaging, and molecular biology. Papers investigating the pathophysiological mechanisms of the nervous system, or reporting on new techniques of interest to computational neuroscientists, including advancements in neural data analysis methods that provide insights into the functioning of the nervous system, are also welcome (in such cases, methodological papers should include applications of new methods with examples illustrating the insights they generate). We expect to publish research at all levels of analysis, from cognition to cellular.

《Journal of Computational Neuroscience》为神经科学的计算与实验研究提供了一个交流平台。该期刊发表原创研究论文、快速通讯和评论文章，涵盖与大脑及神经系统计算相关的理论与实验工作。特别鼓励理论与实验相结合的研究。主要的理论论文应关注与生物神经系统密切相关的问题，而实验论文则需对神经系统的计算功能产生影响，研究方法可以包括解剖学、电生理学、生物物理学、成像技术和分子生物学等多种手段。关于神经系统病理生理机制的研究，或是介绍计算神经科学领域新技术的论文（尤其是那些展示新方法应用及其所带来的新见解的论文）也受到欢迎。我们期待涵盖从认知到细胞的各个分析层面的研究成果在《Journal of Computational Neuroscience》上发表。

Journal of Computational Neuroscience

J Comput Neurosci

Bifurcations of large networks of two-dimensional integrate and fire neurons.

A technique to reduce a full network of this class of neurons to a mean field model, in the form of a system of switching ordinary differential equations, using population density methods and a quasi-steady state approximation to arrive at the mean field system.

Category	Quartile
医学	4
医学, 数学与计算生物学	4
医学, 神经科学	4

Bifurcations of large networks of two-dimensional integrate and fire neurons.

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