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Geometric perspective of linear stability in finite networks of nonlinear oscillators https://arxiv.org/abs/2504.06377 #mathDS

Geometric perspective of linear stability in finite networks of nonlinear oscillators

We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematical approach offers analytical predictions for the linear stability of $q$-states, which include phase synchronization ($q = 0$) and waves with different spatial frequencies ($|q| > 0$). This approach seamlessly incorporates the presence of time delays (represented by phase-lags in the coupling). With this, we are able to analytically determine the specific combination of connectivity and time delays (phase-lags) that leads to any given $q$-state to be linearly stable. This approach offers a geometric perspective of linear stability in finite networks in terms of the connectivity and delays (phase-lag), and it opens a path to designing and controlling the spatiotemporal dynamics of individual oscillator networks.

arXiv.org
April 11, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
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