Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA.
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
Phys Rev Lett. 2019 Oct 18;123(16):164101. doi: 10.1103/PhysRevLett.123.164101.
We use the theory of isostable reduction to incorporate higher order effects that are lost in the first order phase reduction of coupled oscillators. We apply this theory to weakly coupled complex Ginzburg-Landau equations, a pair of conductance-based neural models, and finally to a short derivation of the Kuramoto-Sivashinsky equations. Numerical and analytical examples illustrate bifurcations occurring in coupled oscillator networks that can cause standard phase-reduction methods to fail.
我们使用等稳定性约化理论来包含在耦合振荡器的一阶相约化中丢失的高阶效应。我们将该理论应用于弱耦合的复金兹堡-朗道方程、一对基于电导的神经模型，最后应用于库仑-斯维夏斯基方程的简短推导。数值和分析示例说明了在可能导致标准相约化方法失败的耦合振荡器网络中发生的分岔。
