arXiv subjects

L. A. Smirnov

Publications and source records attributed to L. A. Smirnov.

18 recordsLinked to original sources

arXiv2026

Birth and breakdown of breathing and rotobreathing cyclops states in Kuramoto networks with higher-mode coupling

Cluster synchronization states often serve as organizing centers for collective dynamics, but their destabilization can open unexpected routes to both coherent and incoherent behavior. We study such transitions for cyclops states in globally coupled networks of identical Kuramoto-Sakaguchi rotators with inertia and two-harmonic coupling. Stationary cyclops states consist of two coherent clusters and a solitary oscillator that maintains fixed phase differences with the clusters. Using Floquet analysis and numerical continuation of periodic orbits, we trace bifurcation routes for the birth and breakdown of breathing and rotobreathing cyclops states with nonstationary intercluster phase differences. Breathing cyclops states, born from their stationary counterparts, correspond to bounded oscillations of the intercluster phases. They lose stability via period-doubling bifurcations, which produce phase-split cyclops states whose intercluster motion repeats only after two cycles of the parent breather, or via cluster-destruction bifurcations. Rotobreathing cyclops states, in which the intercluster phase differences undergo full rotations, are not merely the large-amplitude continuation of breathing cyclops states; instead, they form a separate family of nonstationary cyclops dynamics born through global bifurcations involving heteroclinic-contour-like structures of saddle cluster states. We further show that these states have wide, often global, basins of attraction, persist in large odd-sized networks, and contrast sharply with even-sized networks, where stationary multi-cluster states dominate. These results identify higher-harmonic coupling and solitary-oscillator-mediated rotations as generic mechanisms for organizing complex cluster motion in phase oscillator networks.

nlin.PS↗

arXiv2026

From Delay to Inertia and Triadic Interactions: A Predictive Model for Time-Delayed Oscillator Networks

Time-delayed oscillator networks underlie diverse biological and physical systems, yet standard first-order phase reductions fail to capture their high-dimensional collective dynamics. In this Letter, we develop a universal second-order predictive reduction for time-delayed Kuramoto-Daido networks that maps delayed one-dimensional phase dynamics to a delay-free network of two-dimensional rotators. Delay induces effective inertia and triadic interactions, yielding accurate predictions of nontrivial attractors and their collective-state statistics, including splay, cyclops, and chimera states. The reduction reveals a division of roles: inertia organizes higher-dimensional dynamics, whereas triadic terms are crucial for lower-dimensional patterns such as chimeras. Applicable to arbitrary topology, higher harmonics, and intrinsic-frequency heterogeneity, it provides a compact, parameter-explicit reduced model. The same framework also extends to time-delayed amplitude-phase oscillator networks, including swarmalators, yielding analogous reduced equations with emergent inertia and triadic higher-order couplings. This unified and readily deployable description enables systematic prediction and analysis of delay-controlled collective dynamics across oscillator networks.

nlin.PS↗

arXiv2025

Kink-Driven Chimera Motion with Quantized Velocity in a Chain of Interacting Particles

We investigate chimera synchronization of internal oscillator states in a ring of interacting particles, using the damped dc-driven Frenkel--Kontorova chain model as an example. In a system with a spatially periodic potential, a dc external force, and dissipation, kinks spontaneously emerge and stabilize. We show that these kinks induce and govern a collective motion of the entire chimera pattern of internal states along the ring. In particular, the average velocity of this motion depends linearly on the number of kink pairs. This number is effectively determined by localized initial perturbations of particle positions, thereby opening a pathway for controlling macroscopic transport through microscopic excitations.

nlin.PS↗

arXiv2023

Synchronization transitions and sensitivity to asymmetry in the bimodal Kuramoto systems with Cauchy noise

We analyze the synchronization dynamics of the thermodynamically large systems of globally coupled phase oscillators under Cauchy noise forcings with bimodal distribution of frequencies and asymmetry between two distribution components. The systems with the Cauchy noise admit the application of the Ott-Antonsen ansatz, which has allowed us to study analytically synchronization transitions both in the symmetric and asymmetric cases. The dynamics and the transitions between various synchronous and asynchronous regimes are shown to be very sensitive to the asymmetry degree whereas the scenario of the symmetry breaking is universal and does not depend on the particular way to introduce asymmetry, be it the unequal populations of modes in bimodal distribution, the phase delay of the Kuramoto-Sakaguchi model, the different values of the coupling constants, or the unequal noise levels in two modes. In particular, we found that even small asymmetry may stabilize the stationary partially synchronized state, and this may happen even for arbitrarily large frequency difference between two distribution modes (oscillator subgroups). This effect also results in the new type of bistability between two stationary partially synchronized states: one with large level of global synchronization and synchronization parity between two subgroups and another with lower synchronization where the one subgroup is dominant, having higher internal (subgroup) synchronization level and enforcing its oscillation frequency on the second subgroup. For the four asymmetry types, the critical values of asymmetry parameters were found analytically above which the bistability between incoherent and partially synchronized states is no longer possible.

nlin.PS↗

arXiv2022

Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling

Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera and cluster splay states. Yet, understanding which rhythm prevails remains challenging. Here, we address this fundamental question in the context of Kuramoto-Sakaguchi networks of identical rotators with higher-order coupling. Through analysis and numerics, we show that three-cluster splay states with two distinct coherent clusters and a solitary oscillator are the prevalent rhythms in networks with an odd number of units. We denote such tripod patterns cyclops states with the solitary oscillator reminiscent of the Cyclops's eye. As their mythological counterparts, the cyclops states are giants that dominate the system's phase space in weakly repulsive networks with first-order coupling. Astonishingly, the addition of the second or third harmonics to the Kuramoto coupling function makes the cyclops states global attractors practically across the full range of coupling's repulsion. At a more general level, our results suggest clues for finding dominant rhythms in repulsive physical and biological networks.

nlin.AO↗

arXiv2021

Stability of rotatory solitary states in Kuramoto networks with inertia

Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and a phase-lagged coupling. The presence of inertia can induce rotatory dynamics of the phase difference between the solitary oscillator and the coherent cluster. We derive asymptotic stability conditions for such a solitary state as a function of inertia, network size, and phase lag that may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (i) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and (ii) the solitary state can be stable in small-size networks with all repulsive coupling. We also discuss the implications of our stability analysis for the emergence of rotatory chimeras.

nlin.PS↗

arXiv2021

Finite-density-induced motility and turbulence of chimera solitons

We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto-Battogtokh model. We demonstrate that for a finite diffusion stable chimera solitons, namely localized synchronous domain in an infinite asynchronous environment, are possible. The solitons are stable also for finite density of oscillators, but in this case they sway with a nearly constant speed. This finite-density-induced motility disappears in the continuum limit, as the velocity of the solitons is inverse proportional to the density. A long-wave instability of the homogeneous asynchronous state causes soliton turbulence, which appears as a sequence of soliton mergings and creations. As the instability of the asynchronous state becomes stronger, this turbulence develops into a spatio-temporal intermittency.

nlin.PS↗

arXiv2021

Disorder fosters chimera in an array of motile particles

We consider an array of non-locally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonstrate that disorder in oscillators positions leads to a transition from the synchronous to the chimera state. For a static (quenched) disorder we find that the probability of synchrony survival changes, in dependence on the number of particles, from nearly zero at small populations to one in the thermodynamic limit. Furthermore, we demonstrate how the synchrony gets destroyed for randomly (ballistically or diffusively) moving oscillators. We show that, depending on the number of oscillators, there are different scalings of the transition time with this number and the velocity of the units.

nlin.PS↗

arXiv2020

Appearance of chaos and hyperchaos in evolving pendulum network

The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled oscillators. In this paper, we study the emergence of spatio-temporal chaos in chains of locally coupled identical pendulums with constant torque. The study of the scenarios of the emergence (disappearance) and properties of chaos is done as a result of changes in: (i) the individual properties of elements due to the influence of dissipation in this problem, and (ii) the properties of the entire ensemble under consideration, determined by the number of interacting elements and the strength of the connection between them. It is shown that an increase of dissipation in an ensemble with a fixed coupling force and elements number can lead to the appearance of chaos as a result of a cascade of period doubling bifurcations of periodic rotational motions or as a result of invariant tori destruction bifurcation. Chaos and hyperchaos can occur in an ensemble by adding or excluding one or more elements. Moreover, chaos arises hard, since in this case the control parameter is discrete. The influence of the coupling strength on the occurrence of chaos is specific. The appearance of chaos occurs with small and intermediate coupling and is caused by the overlap of the various out-of-phase rotational modes regions existence. The boundaries of these areas are determined analytically and confirmed in a numerical experiment. Chaotic regimes in the chain do not exist if the coupling strength is strong enough.

nlin.CD↗

arXiv2020

Generation of entangled states of light using discrete solitons in waveguide arrays

We study the quantum properties of light propagating through an array of coupled nonlinear waveguides and forming a discrete soliton. We demonstrate that it is possible to use certain types of quasi-solitons to form continuous variables entanglement between the certain pair of waveguides. This entanglement generation process occurs even with a very large number of photons in the laser field used, so it does not require a special material with an extremely high nonlinearity coefficient. Also absorption in the waveguide media does not influence it too much.

quant-ph↗

arXiv2020

Synchronization structures in the chain of rotating pendulums

The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures, in locally coupled identical pendulum-type elements chains that describe the behavior of phase-locked-loop systems, distributed Josephson junctions, coupled electrical machines, etc. The control parameters in the considered chains are: dissipation, coupling strength, and number of elements. In the system under consideration, the realized modes are synchronous in frequency and synchronous (in-phase) or asynchronous (out-of-phase) in phase. In the low dissipation case, the in-phase synchronous rotational regime instability region boundaries are theoretically found and the bifurcations leading to the loss of its stability are determined. The analysis was carried out for chains of arbitrary length. The existence of various out-of-phase synchronous rotational modes types is revealed: completely asynchronous in phases and the cluster in-phase synchronization regime. Regularities of transitions from one type of out-of-phase synchronous mode to another are established. It was found that at certain coupling parameter values, the coexistence of stable in-phase and out-of-phase synchronous modes is possible. It was found that for arbitrary chain length, the number of possible stable out-of-phase modes is always one less than the chain elements number. Analytical results are confirmed by numerical simulations.

nlin.CD↗

arXiv2020

Bogoliubov-Cherenkov Radiation in an Atom Laser

We develop a simple yet powerful technique to study Bogoliubov-Cherenkov radiation by producing a pulsed atom laser from a strongly confined Bose-Einstein condensate. Such radiation results when the atom laser pulse falls past a Bose-Einstein condensate at high-hypersonic speeds, modifying the spatial profile to display a characteristic twin jet structure and a complicated interference pattern. The experimental observations are in excellent agreement with mean-field numerical simulations and an analytic theory. Due to the highly hypersonic regime reached in our experiment, this system offers a highly controllable platform for future studies of condensed-matter analogs of quantum electrodynamics at ultrarelativistic speeds.

cond-mat.quant-gas↗

arXiv2020

Symmetry broken states in an ensemble of globally coupled pendulums

We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of the community elements. There exists the wide variety of in-phase and out-of-phase regimes. Many of these states appear due to broken symmetry. In the case of small dissipation our theoretical analysis allows one to find the boundaries of the instability domain of in-phase rotational mode for ensembles with arbitrary number of pendulums, describe all arising out-of-phase rotation modes and study in detail their stability. For the system of three elements parameter sets corresponding to the unstable in-phase rotations we find a number of out-of-phase regimes and investigate their stability and bifurcations both analytically and numerically. As a result, we obtain a sufficiently detailed picture of the symmetry breaking and existence of various regular and chaotic states.

nlin.CD↗

arXiv2019

Generation of gaussian entangled states of light in an array of nonlinear waveguides

We investigate the process of entangled state of light generation while propagation along a one dimensional array of single-mode nonlinear waveguides. We consider a situation when entanglement is formed due to spontaneous parametric down-conversion of the pump which is present only in a signal waveguide. In the considered process the generated state of light is multi-mode squeezed. We demonstrate that starting from certain distance of light propagation only pairs of waveguides, located symmetrically with respect to the pumped one, occur to be entangled. Also there is an optimal pump amplitude for which the formed quantum correlations are most pronounced. Entanglement for multi-mode squeezed states may be very sensitive for phase fluctuations in the pump. We investigate the influence of such noise on the discussed process. We demonstrate that for situation of generation of few photon entangled states the influence of phase fluctuations is negligible. But it dramatically increase with the growth of average photon numbers in the formed quantum states.

quant-ph↗

arXiv2018

Variety of rotation modes in a small chain of coupled pendulums

This article studies the rotational dynamics of three identical coupled pendulums. There exist two parameter areas where the in-phase rotational motion is unstable and out-of-phase rotations are realized. Asymptotic theory is developed that allows to analytically identify boarders of instability areas of in-phase rotation motion. It is shown that out-of-phase rotations are the result of parametric instability of in-phase motion. Complex out-of-phase rotations are numerically found and their stability and bifurcations are defined. It is demonstrated that emergence of chaotic dynamics happens due period doubling bifurcation cascade. The detail scenario of symmetry breaking is presented. The development of chaotic dynamics leads to origin of two chaotic attractors of different types. The first one is characterized by the different phases of all pendulums. In the second case the phases of two pendulums are equal, and the phase of the third one is different. This regime with partial symmetry breaking is a chaotic chimera.

nlin.CD↗

arXiv2018

Solitary synchronization waves in distributed oscillators populations

We demonstrate existence of solitary waves of synchrony in one-dimensional arrays of identical oscillators with Laplacian coupling. Coarse-grained description of the array leads to nonlinear equations for the complex order parameter, in the simplest case to lattice equations similar to those of the discrete nonlinear Schrodinger lattice. Close to full synchrony, we find solitary waves for the order parameter perturbatively, starting from the known phase compactons and kovatons; these solution are extended numerically to the full domain of possible synchrony levels. For non-identical oscillators, existence of dissipative solitons is demonstrated.

nlin.PS↗

arXiv2016

Influence of classic noise on entangled state formation in parametric systems

A study of "high temperature" entangled states in a system of two parametrically coupled quantum oscillators placed into independent thermal baths is performed taking into account partially coherent parametric pump. Processes in an open system are considered based on the Heisenberg-Langevin formalism. We obtain a closed system of equations for the averaged quadratic correlation functions in quantum stochastic problem as a result of Markov processes approximation. On the basis of numerical calculations the dynamics of the logarithmic negativity, which is the measure of entanglement in the system, is investigated. It is shown that the partial coherence of the parametric pump makes the lifetime of the entangled states finite. The threshold characteristics of the formation and existence of these states are specified.

quant-ph↗

arXiv2016

Chimera patterns in the Kuramoto-Battogtokh model

Kuramoto and Battogtokh [Nonlinear Phenom. Complex Syst. 5, 380 (2002)] discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After reformulation in terms of local order parameter, the problem can be reduced to partial differential equations. We find uniformly rotating periodic in space chimera patterns as solutions of a reversible ordinary differential equation, and demonstrate a plethora of such states. In the limit of neutral coupling they reduce to analytical solutions in form of one- and two-point chimera patterns as well as localized chimera solitons. Patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only simplest chimeras with one synchronous region are stable.

nlin.PS↗