Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, 0745, New Zealand.
J Math Neurosci. 2012 Mar 14;2(1):5. doi: 10.1186/2190-8567-2-5.
We consider a coupled, heterogeneous population of relaxation oscillators used to model rhythmic oscillations in the pre-Bötzinger complex. By choosing specific values of the parameter used to describe the heterogeneity, sampled from the probability distribution of the values of that parameter, we show how the effects of heterogeneity can be studied in a computationally efficient manner. When more than one parameter is heterogeneous, full or sparse tensor product grids are used to select appropriate parameter values. The method allows us to effectively reduce the dimensionality of the model, and it provides a means for systematically investigating the effects of heterogeneity in coupled systems, linking ideas from uncertainty quantification to those for the study of network dynamics.
我们考虑了一个用于模拟前 Bötzinger 复合体中节律性振荡的耦合、异质的松弛振荡器群体。通过从该参数值的概率分布中选择用于描述异质性的特定参数值，可以以计算效率的方式研究异质性的影响。当有多个参数存在异质性时，使用全或稀疏张量积网格来选择适当的参数值。该方法允许我们有效地降低模型的维数，并为系统地研究耦合系统中的异质性提供了一种手段，将不确定性量化的思想与网络动力学的研究联系起来。
