105 citations · 162 across the 7 of their papers we have counts for
7 papers
Kinetic description of one-dimensional stochastic dynamics with small inertia
Denis S. Goldobin, Lyudmila S. Klimenko, Irina V. Tyulkina +2
We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (pha…
Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise
Anastasiya V. Dolmatova, Irina V. Tyulkina, Denis S. Goldobin
We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussi…
Four approaches for description of stochastic systems with small and finite inertia
Evelina V. Permyakova, Lyudmila S. Klimenko, Irina V. Tyulkina +1
We analyse four approaches to elimination of a fast variable, which are applicable to systems like passive Brownian particles: (i) moment formalism, (ii) corresponding cumulant for…
Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory
Irina V. Tyulkina, Denis S. Goldobin, Lyudmila S. Klimenko +2
The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in 2D XY arrays is addressed. The system is modeled as a plane structure of identical sin…
Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions
Irina V. Tyulkina, Denis S. Goldobin, Arkady Pikovsky
We study a numerical instability of direct simulations with truncated equation chains for the "circular cumulant" representation and two approaches to its suppression. The approach…
Collective mode reductions for populations of coupled noisy oscillators
Denis S. Goldobin, Irina V. Tyulkina, Lyudmila S. Klimenko +1
We analyze accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations…
Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
Irina V. Tyulkina, Denis S. Goldobin, Lyudmila S. Klimenko +1
We develop an approach for the description of the dynamics of large populations of phase oscillators based on "circular cumulants" instead of the Kuramoto-Daido order parameters. I…