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G. V. Osipov

Publications and source records attributed to G. V. Osipov.

At least 19 recordsLinked to original sources
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↗
arXiv2025

Stationary and switching synchronization regimes in an ensemble of four nonidentical phase oscillators with repulsive couplings

This study investigates the collective dynamics (phase synchronization, instantaneous frequencies synchronization and mean frequencies synchronization) in an ensemble of four nonidentical phase oscillators with repulsive coupling. We use the Kuramoto-Sakaguchi system of ordinary differential equations as our mathematical model. Depending on the coupling strength in the presence of a small mismatch of the natural frequencies, all possible modes of frequency synchronization were found: 4:0 (global), 3:1, 2:2, 2:1:1 (cluster). It is shown that these regimes can be classified into two main types depending on the evolution of the instantaneous frequencies: stationary (4:0 and 2:2), characterized by constancy of phase ratios and instantaneous frequencies, and switching (3:1 and 2:1:1), in which metastable processes with periodic switching of synchronous states are observed: for different time intervals, different types of locking of instantaneous frequencies of oscillator pairs and different types of phase ratios were observed. For the 4:0 and 2:2 regimes, analytical expressions for the synchronization frequencies were derived. The presence of bistability has been revealed depending on the initial conditions of different synchronous regimes at the same parameters: sets of individual frequencies and value of coupling strength.

nlin.PS↗
arXiv2024

Synchronization and desynchronization in ensembles of mobile agents

Mechanisms of emergence and destruction are analyzed, as well as characteristics of synchronous and asynchronous modes of behavior of ensembles (swarms) of interacting mobile agents moving according to chaotic phase trajectories of Rossler and Lorenz systems. The possibility of organizing sequential and parallel motion of agents based on the effect of chaotic phase synchronization is demonstrated.

nlin.CD↗
arXiv2023

Switching activity in an ensemble of excitable neurons

The paper proposes two dynamical systems based on the generalized Lotka-Volterra model of three excitable elements interacting through excitatory couplings. It is shown that for some values of the coupling parameters in the phase space of systems, there are heteroclinic cycles containing three or six saddle equilibrium states and heteroclinic curves connecting them. Under certain external stimuli that transfer the system from a stable zero equilibrium state to a small neighborhood of the heteroclinic cycle, the phase trajectory will alternately visit the neighborhood of saddle equilibrium states (possibly more than once), after which it will return to its initial state. The described behavior is proposed to be used to simulate switching activity in neural ensembles. Different transients are determined by different external stimuli. The passage of the phase point of the system near the saddle equilibrium states included in the heteroclinic circuit is proposed to be interpreted as activation of the corresponding element.

nlin.CD↗
arXiv2023

Synchronization and movement control of an ensemble of mobile agents

This article suggests ways to implement sequential, parallel and in the form of a given configuration of the movement of an ensemble (swarm) of mobile agents using the effect of chaotic phase synchronization. The possibility of controlling the movement of the ensemble is shown and the stability conditions of the obtained structures are determined.

nlin.AO↗
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↗
arXiv2021

Dynamics in a phase model of half-center oscillator: two neurons with excitatory coupling

A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of dynamics, characteristic for central pattern generators: respectively, in-phase, anti-phase synchronous oscillations and quiescence, and study various bifurcation transitions between all these states. Suggested model can serve as a building block of specific complex central pattern generators for studies of rhythmic activity and information processing in animals and humans.

math.DS↗
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

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↗
arXiv2018

Desynchronization in heterogeneous networks due to uniform exposure

We study synchronization and rhythmic patterns generated in the heterogeneous cluster of FitzHugh$-$Nagumo oscillators with transition between self-oscillating and excitable elements. Such cluster models the sinoatrial node of the heart, and the particular point of focus is the role of different physiological responses to mechanical stress: stretch-activated current and conductivity change. The comparison between them finds the difference which can serve to identify the dominant mechanism in specific experimental situations.

nlin.PS↗
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↗
arXiv2018

Spiral attractors as the root of a new type of "bursting activity" in the Rosenzweig-MacArthur model

We study the peculiarities of spiral attractors in the Rosenzweig-MacArthur model, that describes dynamics in a food chain "prey-predator-superpredator". It is well-known that spiral attractors having a "teacup" geometry are typical for this model at certain values of parameters for which the system can be considered as slow-fast system. We show that these attractors appear due to the Shilnikov scenario, the first step in which is associated with a supercritical Andronov-Hopf bifurcation and the last step leads to the appearance of a homoclinic attractor containing a homoclinic loop to a saddle-focus equilibrium with two-dimension unstable manifold. It is shown that the homoclinic spiral attractors together with the slow-fast behavior give rise to a new type of bursting activity in this system. Intervals of fast oscillations for such type of bursting alternate with slow motions of two types: small amplitude oscillations near a saddle-focus equilibrium and motions near a stable slow manifold of a fast subsystem. We demonstrate that such type of bursting activity can be either chaotic or regular.

nlin.CD↗