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The control of frequency of a conditional oscillator simultaneously subjected to multiple oscillatory inputs.

机译：条件振荡器的频率控制同时受到多个振荡输入的影响。

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摘要

A conditional oscillator is one that requires input to oscillate. An example of such is the gastric mill network of the stomatogastric ganglion of the crab Cancer borealis which requires modulatory input from outside the stomatogastric ganglion and fast input from the pyloric network of the animal in order to become active. This dissertation studies how the frequency of the gastric mill network is determined when it is simultaneously subjected to two different rhythmic inputs whose timing may be mismatched. We derive a mathematical model of the gastric mill network and deduce that the difference in timing between the pyloric and modulatory inputs is crucial in determining what effect it will have on the frequency of the gastric mill network. Over a certain range of the time mismatch; the pyloric input plays no role in determining the network frequency, while in another range of the time mismatch, both inputs work together to determine the frequency. The existence and stability of periodic solutions to the modeling set of equations are obtained analytically using geometric singular perturbation theory and an analytic approximation of the frequency is obtained. The results are validated through numerical simulations of the model and are shown to extend to a detailed Hodgkin-Huxley type compartmental model of the gastric mill network. Comparisons to experiments are also presented.
机译：条件振荡器是需要输入振荡的振荡器。这样的一个例子是蟹癌的胃的胃胃神经节的胃磨网，其需要来自胃胃神经节外部的调节性输入和来自动物的幽门网的快速输入以变得活跃。本论文研究了在同时受到时间可能不匹配的两个不同的节奏输入的作用下，如何确定胃磨网的频率。我们推导了胃磨网的数学模型，并推断幽门和调节输入之间的时间差异对于确定其对胃磨网的频率有何影响至关重要。在一定时间范围内不匹配；幽门输入对确定网络频率不起作用，而在另一个时间失配范围内，两个输入共同确定频率。利用几何奇异摄动理论解析地获得了方程组的周期解的存在性和稳定性，并获得了频率的解析近似。该结果通过模型的数值模拟得到了验证，并被证明可以扩展到胃磨网的详细的霍奇金-赫克斯利型隔室模型。还提供了与实验的比较。

著录项

  • 作者

    Ambrosio, Christina L.;

  • 作者单位

    New Jersey Institute of Technology.;

  • 授予单位 New Jersey Institute of Technology.;
  • 学科 Mathematics.;Biology Neuroscience.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 134 p.
  • 总页数 134
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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