2021/09/04 by Sara Ameli, Ameli, Sara, Keivan Aghababaei Samani +1
Computer Science · Engineering · Environmental Science · #Adaptation and Self-Organizing Systems (nlin.AO) #Ecosystem dynamics and resilience #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.2109.01848
openalex publication_date 2021/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the global bifurcations of frequency weighted Kuramoto model in low-dimension for network of fully connected oscillators. To study the effect of non-zero-centered frequency distribution, we consider two symmetric Lorentzians as an example. We derive the stability diagram of the system and show that the infinite-dimensional problem reduces to a flow in four dimensions. Using the system symmetries, it can be further reduced to two dimensions. Using this analytic framework, we obtain bifurcation boundaries of the system, which is compatible with our numeric simulations. We show that the system has three types of transitions to synchronized state for different parameters of the frequency distribution: (1) a two-step transition, representative of standing waves, (2) a continuous transition, as in the classical Kuramoto model, and (3) a first-order transition with hysteresis. Numerical simulations are also conducted to confirm analytic results.