Volcano transition in populations of phase oscillators with random nonreciprocal interactions

Author:

Diego Pazó, Rafael Gallego

Keyword:

Nonlinear Sciences, Adaptation and Self-Organizing Systems, Adaptation and Self-Organizing Systems (nlin.AO), Disordered Systems and Neural Networks (cond-mat.dis-nn)

journal:

Phys. Rev. E 108, 014202 (2023)

date:

2023-06-12 16:00:00

Abstract

Populations of heterogeneous phase oscillators with frustrated random interactions exhibit a quasi-glassy state in which the distribution of local fields is volcano-shaped. In a recent work [Phys. Rev. Lett. 120, 264102 (2018)] the volcano transition was replicated in a solvable model using a low-rank, random coupling matrix $\mathbf M$. We extend here that model including tunable nonreciprocal interactions, i.e. ${\mathbf M}^T\ne \mathbf M$. More specifically, we formulate two different solvable models. In both of them the volcano transition persists if matrix elements $M_{jk}$ and $M_{kj}$ are enough correlated. Our numerical simulations fully confirm the analytical results. To put our work in a wider context, we also investigate numerically the volcano transition in the analogous model with a full-rank random coupling matrix.

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