论文标题
强耦合振荡器的耦合函数的高阶精度计算
High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators
论文作者
论文摘要
我们开发了一个通用框架，用于识别耦合振荡器有限种群的相减小方程，该方程的有效远远超出了弱耦合近似值。该策略代表了[Wilson and Ermentrout，phys。 Rev. Lett 123，164101（2019）]，并产生耦合函数，这些函数在任意类型的耦合（例如扩散，间隙结构，化学突触）的耦合强度的高阶精度上有效。这些耦合函数可用于了解其相位差异的潜在高维非线性振荡器的行为。提出的公式准确地复制了随着耦合强度的增加而出现的非线性分叉，并且在远远超出可以使用经典弱耦合假设的方案的方案中有效。我们通过两个示例证明了方法的性能。首先，我们使用扩散耦合的复杂的金茨堡 - 兰道（CGL）模型，并证明我们的理论准确地预测分叉远远超出了现有耦合理论的范围。其次，我们使用丘脑神经元的基于现实的电导模型，并表明我们的理论正确预测了非垂直突触耦合的渐近相差异。在这两个示例中，我们的理论都准确地捕获了弱耦合理论的模型行为。
We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from [Wilson and Ermentrout, Phys. Rev. Lett 123, 164101 (2019)] and yields coupling functions that are valid to higher-order accuracy in the coupling strength for arbitrary types of coupling (e.g., diffusive, gap-junction, chemical synaptic). These coupling functions can be used to understand the behavior of potentially high-dimensional, nonlinear oscillators in terms of their phase differences. The proposed formulation accurately replicates nonlinear bifurcations that emerge as the coupling strength increases and is valid in regimes well beyond those that can be considered using classic weak coupling assumptions. We demonstrate the performance of our approach through two examples. First, we use diffusively coupled complex Ginzburg-Landau (CGL) model and demonstrate that our theory accurately predicts bifurcations far beyond the range of existing coupling theory. Second, we use a realistic conductance-based model of a thalamic neuron and show that our theory correctly predicts asymptotic phase differences for non-weak synaptic coupling. In both examples, our theory accurately captures model behaviors that weak coupling theories can not.
