arXiv subjects

K. P. O'Keeffe

Publications and source records attributed to K. P. O'Keeffe.

5 recordsLinked to original sources

arXiv2026

Arithmetic of the sync basin for pulse-coupled oscillato

A population of $N$ identical pulse-coupled oscillators ultimately settles into one of two outcomes: full synchrony or a state of co-existing synchronized clusters. We show that which outcome occurs is controlled by the prime factorization of $N$. At the critical charging curve --- linear, the boundary between the synchronizing and clustering regimes --- the synchronization basin acquires exact arithmetic structure. The synchronization probability is $\Psync=A_{N,1}/N^N$ for all $N$, where $A_{N,1}$ satisfies an exact recurrence relation. For prime $N$, $A_{N,1}=N^N-1$ giving the closed form $\Psync=1-1/N^N$; for composite $N$, the observed asymptotic scaling is $1-\Psync\sim C_m N^{-(m-1)}$, where $m$ is the smallest prime divisor. The result adds a new member to the atlas of exotic basin geometries: alongside fractal, riddled, and tentacled basins, we now have a basin that is arithmetic.

nlin.AO↗

arXiv2026

Synchrony by Birth and Death

A population of oscillators typically synchronizes because coupling pulls their phases together. Here we consider malthusian oscillators whose coupling is demographic: oscillators are born and die at rates determined by their phases, generating an effective coupling without any phase velocity interaction. We find this coupling can synchronize a population, select a collective frequency, and produce a nongeneric fourth-root onset of coherence. These collective dynamics admit an exact reduction: a population with $m$ frequency classes reduces to $3m$ ordinary differential equations. This is the malthusian analogue of the Ott--Antonsen reduction for Kuramoto oscillators.

nlin.AO↗

arXiv2026

Coupling-split clusters in a swarmalator model with uniform coupling disorder

We study the one-dimensional swarmalator model in which the phase coupling $K_i'$ is drawn from a uniform distribution. Our main result is a static coupling-split cluster, in which the population partitions across the threshold $K'=0$ that separates positively coupled ($K_i'>0$) from negatively coupled ($K_i'<0$) swarmalators, with smaller order parameter $s=μ/γ$ set by the positive-coupling excess. The familiar async, phase-wave, and sync states persist, but each stability boundary feels a different part of the distribution: async the mean same-coordinate response, sync the most negatively coupled particle, and the phase wave the full density through a logarithmic characteristic equation. At a cusp where its Hopf and real-eigenvalue branches meet, the phase-wave dispersion has a double zero -- the spectral signature of a Bogdanov--Takens point -- and simulations nearby show a small-amplitude breathing limit cycle. For supports containing strongly negatively coupled particles the order parameters instead oscillate persistently.

nlin.AO↗

arXiv2026

Time delay in the 1d swarmalator model

We study the 1d swarmalator model augmented with time delayed coupling. Along with the familiar sync, async, and phase wave states, we find a family of unsteady states where the order parameters are time periodic, sometimes with clean oscillations, sometimes with irregular vacillations. The unsteady states are born in two ways: via a Hopf bifurcation from the phase wave, and a zero eigenvalue bifurcation from the async state. We find both of these boundary curves analytically. A surprising result is that stabilities of the async and sync states are independent of the delay τ; they depend only on the coupling strength.

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arXiv2022

Sync and swarm: solvable model of non-identical swarmalators

We study a model of non-identical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces four collective states: asynchrony, sync clusters, vortex-like phase-waves, and a mixed state. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical nanomotors, and groups of drones. A generalized Ott-Antonsen ansatz provides the first analytic description of these states and conditions for their existence. We show how this approach may be used in studies of active matter and related disciplines.

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