arXiv subjects

Yuri Maistrenko

Publications and source records attributed to Yuri Maistrenko.

18 recordsLinked to original sources

arXiv2026

Chaotic Switching In The Minimal Pendula Network

We report the chaotic switching phenomenon in the minimal $N = 3$ pendula network with global coupling. Analyzing the stability conditions of the chimera states and their dependence on the parameters, three scenarios of chaotic switchings are identified: 1) a riddling bifurcation scenario, where an unstable periodic orbit inside the chimera manifold becomes transversally unstable, 2) a blowout bifurcation scenario, where the switching is caused by the transverse destabilization of the chaotic chimera with respect to its manifold, and 3) switchings between "laminar" saddle chimeras within a global "turbulent" attractor. The results are obtained based on the detailed examination of the existing regimes including chimera states, limit cycles and fixed points, their multistability and switching regime. In the parameter regions where the chaotic chimeras coexist with stable non-chaotic solutions, the switching trajectory can eventually escape to a stable solution, causing an additional unpredictability in the system behavior, as it is difficult to predict the escaping moment.

nlin.CD↗

arXiv2021

Generalized splay states in phase oscillator networks

Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized $m$-splay states constituting a special subclass of phase-locked states with vanishing $m$th order parameter. Such states typically manifest incoherent dynamics, and they often create high-dimensional families of solutions (splay manifolds). For a general class of phase oscillator networks, we provide explicit linear stability conditions for splay states and exemplify our results with the well-known Kuramoto-Sakaguchi model. Importantly, our stability conditions are expressed in terms of just a few observables such as the order parameter or the trace of the Jacobian. As a result, these conditions are simple and applicable to networks of arbitrary size. We generalize our findings to phase oscillators with inertia and adaptively coupled phase oscillator models.

math.DS↗

arXiv2021

Chimera states for directed networks

We demonstrate that chimera behavior can be observed in ensembles of phase oscillators with unidirectional coupling. For a small network consisting of only three identical oscillators (cyclic triple), tiny {\it chimera islands} arise in the parameter space. They are surrounded by developed chaotic switching behavior caused by a collision of rotating waves propagating in opposite directions. For larger networks, as we show for hundred oscillators (cyclic century), the islands merge into a single {\it chimera continent} which incorporates the world of chimeras of different configuration. The phenomenon inherits from networks with intermediate ranges of the unidirectional coupling and it diminishes as it decreases.

nlin.CD↗

arXiv2020

Solitary states in the mean-field limit

We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models.

nlin.AO↗

arXiv2020

Minimal Chimera States in Phase-Lag Coupled Mechanical Oscillators

We obtain experimental chimera states in the minimal network of three identical mechanical oscillators (metronomes), by introducing phase-lagged all-to-all coupling. For this, we have developed a real-time model-in-the-loop coupling mechanism that allows for flexible and online change of coupling topology, strength and phase-lag. The chimera states manifest themselves as a mismatch of average frequency between two synchronous and one desynchronized oscillator. We find this kind of striking chimeric behavior is robust in a wide parameter region. At other parameters, however, chimera state can lose stability and the system behavior manifests itself as a heteroclinic switching between three saddle-type chimeras. Our experimental observations are in a qualitative agreement with the model simulation.

nlin.AO↗

arXiv2020

Spiral wave chimeras for coupled oscillators with inertia

We report the appearance and the metamorphoses of spiral wave chimera states in coupled phase oscillators with inertia. First, when the coupling strength is small enough, the system behavior resembles classical two-dimensional (2D) Kuramoto-Shima spiral chimeras with bell-shape frequency characteristic of the incoherent cores. As the coupling increases, the cores acquire concentric regions of constant time-averaged frequencies, the chimera becomes quasiperiodic. Eventually, with a subsequent increase in the coupling strength, only one such region is left, i.e., the whole core becomes frequency-coherent. An essential modification of the system behavior occurs, when the parameter point enters the so-called solitary} region. Then, isolated oscillators are normally present on the spiral core background of the chimera states. These solitary oscillators do not participate in the common spiraling around the cores; instead, they start to oscillate with different time-averaged frequencies (Poincaré winding numbers). The number and the disposition of solitary oscillators can be any, given by the initial conditions. At a further increase in the coupling, the spiraling disappears, and the system behavior passes to a sort of spatiotemporal chaos.

nlin.AO↗

arXiv2018

Network-induced multistability: Lossy coupling and exotic solitary states

The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. In the latter case, the ongoing transition to distributed renewable energy sources is leading to a proliferation of dynamical actors. The desynchronization of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a focus of power grid research in recent years. In this letter we uncover that the non-linear stability against large perturbations is dominated and threatened by the presence of \textit{solitary states} in which individual actors desynchronise. Remarkably, when taking physical losses in the network into account, the back-reaction of the network induces new {\it exotic} solitary states in the individual actors, and the stability characteristics of the synchronous state are dramatically altered. These novel effects will have to be explicitly taken into account in the design of future power grids, and their existence poses a challenge for control. While this letter focuses on power grids, the form of the coupling we explore here is generic, and the presence of new states is very robust. We thus strongly expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.

nlin.AO↗

arXiv2018

Self-propelled chimeras

The synchronization of self-propelled particles (SPPs) is a fascinating instance of emergent behavior in living and man-made systems, such as colonies of bacteria, flocks of birds, robot ensembles, and many others. The recent discovery of chimera states in coupled oscillators opens up new perspectives and indicates that other emergent behaviors may exist for SPPs. Indeed, for a minimal extension of the classical Vicsek model we show the existence of chimera states for SPPs, i.e., one group of particles synchronizes while others wander around chaotically. Compared to chimeras in coupled oscillators where the site position is fixed, SPPs give rise to new distinctive forms of chimeric behavior. We emphasize that the found behavior is directly implied by the structure of the deterministic equation of motion and is not caused by exogenous stochastic excitation. In the scaling limit of infinitely many particles, we show that the chimeric state persists. Our findings provide the starting point for the search or elicitation of chimeric states in real world SPP systems.

nlin.AO↗

arXiv2017

Spatio-temporal complexity in dual delay nonlinear laser dynamics: chimeras and dissipative solitons

We demonstrate for a nonlinear photonic system that two highly asymmetric feedback delays can induce a variety of emergent patterns which are highly robust during the system's global evolution. Explicitly, two-dimensional chimeras and dissipative solitons become visible upon a space-time transformation. Switching between chimeras and dissipative solitons requires only adjusting two system parameters, demonstrating self-organization exclusively based on the system's dynamical properties. Experiments were performed using a tunable semiconductor laser's transmission through a Fabry-Perot resonator resulting in an Airy function as nonlinearity. Resulting dynamics were band-pass filtered and propagated along two feedback paths whose time delays differ by two orders of magnitude. An excellent agreement between experimental results and theoretical model given by modified Ikeda equations was achieved.

physics.optics↗

arXiv2017

Solitary states for coupled oscillators

We demonstrate that solitary states can be widely observed for networks of coupled oscillators with local, non-local and global couplings, and they preserve in both thermodynamic and Hamiltonian limits. We show that depending on units' and network's parameters, different types of solitary states occur, characterized by the number of isolated oscillators and the disposition in space. The creation of solitary states through the homoclinic bifurcation is described and the regions of co-existence of obtained states and typical examples of dynamics have been identified. Our analysis suggests that solitary states can be observed in a wide class of networks relevant to various real-world systems.

nlin.CD↗

arXiv2017

Multiple scroll wave chimera states

We refer the appearance of three-dimensional (3D) multiheaded chimera states that display cascades of self-organized spatiotemporal patterns of coexisting coherence and incoherence. We demonstrate that number of the incoherent chimera's domains can grow additively under appropriate varying the system parameters generating thereby head-adding cascades of the scroll wave chimeras. The phenomenon is derived for Kuramoto model of N identical phase oscillators placed in the 3D cube with periodic boundary conditions, parameters are coupling radius $r$ and phase lag $α$. To obtain the multiheaded chimeras, we perform the so-called 'cloning procedure' as follows: choose a sample single-headed 3D chimera state, make appropriate scale transformation, and put some number of copies of them into the unit cube. After, start numerical simulations with slightly perturbed initial conditions for long enough time to confirms or denies the state existence and stability. It is found, by this a way, that multiple scroll wave chimeras including those with incoherent rolls, Hopf links and trefoils admit this sort of multiheaded regeneration. On the other hand, multiple 3D chimeras without spiral rotations, like coherent and incoherent balls, tubes, crosses, and layers appear to be unstable under are destroyed rather fast even with any small perturbations.

nlin.PS↗

arXiv2016

The smallest chimera states

We demonstrate that chimera behavior can be observed in small networks consisting of three identical oscillators, with mutual all-to-all coupling. Three different types of chimeras, characterized by the coexistence of two coherent oscillators and one incoherent oscillator (i.e. rotating with another frequency) have been identified, where the oscillators show periodic (two types) and chaotic (one type) behaviors. Typical bifurcations at the transitions from full synchronization to chimera states and between different types of chimeras have been described. Parameter regions for the chimera states are obtained in the form of Arnold tongues, issued from a singular parameter point. Our analysis suggests that chimera states can be observed in small networks, relevant to various real-world systems.

nlin.CD↗

arXiv2016

Delayed-feedback chimera states: Forced multiclusters and stochastic resonance

A nonlinear oscillator model with negative time-delayed feedback is studied numeri- cally under external deterministic and stochastic forcing. It is found that in the unforced system complex partial synchronization patterns like chimera states as well as salt-and-pepper like soli- tary states arise on the route from regular dynamics to spatio-temporal chaos. The control of the dynamics by external periodic forcing is demonstrated by numerical simulations. It is shown that one-cluster and multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. If a stochastic component is superimposed to the determin- istic external forcing, chimera states can be induced in a way similar to stochastic resonance, they appear, therefore, in regimes where they do not exist without noise.

nlin.AO↗

arXiv2014

Laser Chimeras as a paradigm for multi-stable patterns in complex systems

Chimera is a rich and fascinating class of self-organized solutions developed in high dimensional networks having non-local and symmetry breaking coupling features. Its accurate understanding is expected to bring important insight in many phenomena observed in complex spatio-temporal dynamics, from living systems, brain operation principles, and even turbulence in hydrodynamics. In this article we report on a powerful and highly controllable experiment based on optoelectronic delayed feedback applied to a wavelength tunable semiconductor laser, with which a wide variety of Chimera patterns can be accurately investigated and interpreted. We uncover a cascade of higher order Chimeras as a pattern transition from N to N - 1 clusters of chaoticity. Finally, we follow visually, as the gain increases, how Chimera is gradually destroyed on the way to apparent turbulence-like system behaviour.

physics.optics↗

arXiv2014

Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction

We discuss the desynchronization transition in networks of globally coupled identical oscillators with attractive and repulsive interactions. We show that, if attractive and repulsive groups act in antiphase or close to that, a solitary state emerges with a single repulsive oscillator split up from the others fully synchronized. With further increase of the repulsing strength, the synchronized cluster becomes fuzzy and the dynamics is given by a variety of stationary states with zero common forcing. Intriguingly, solitary states represent the natural link between coherence and incoherence. The phenomenon is described analytically for phase oscillators with sine coupling and demonstrated numerically for more general amplitude models.

nlin.AO↗

arXiv2012

Transition from spatial coherence to incoherence in coupled chaotic systems

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wave-like profiles and study the transition from coherence to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings we consider time-discrete as well as time-continuous chaotic models realized as logistic map and Rössler or Lorenz system, respectively. Thereby we establish the coherence-incoherence transition in networks of coupled identical oscillators.

nlin.CD↗

arXiv2011

Loss of coherence in dynamical networks: spatial chaos and chimera states

We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.

nlin.AO↗

arXiv2006

From synchronization to Lyapunov exponents and back

The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble- rather than time-averages. The approach passes through the identification of locally stable and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy with generalized synchronization. The method is then applied to a periodically forced chaotic oscillator to show that the modulus of the Lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase-synchronization. The analytical calculations are carried out for a model, the generalized special flow, that we construct as a simplified version of the periodically forced Rossler oscillator.

nlin.CD↗