@article{AbelFlachPikovskij1998, author = {Abel, Markus and Flach, S. and Pikovskij, Arkadij}, title = {Localisation in a coupled standard map lattice}, year = {1998}, abstract = {We study spatially localized excitations in a lattice of coupled standard maps. Time-periodic solutions (breathers) exist in a range of coupling that is shown to shrink as the period grows to infinity, thus excluding the possibility of time-quasiperiodic breathers. The evolution of initially localized chaotic and quasiperiodic states in a lattice is studied numerically. Chaos is demonstrated to spread}, language = {en} } @article{AbelFlachPikovskij1998, author = {Abel, Markus and Flach, S. and Pikovskij, Arkadij}, title = {Localization in a coupled standard map lattice}, year = {1998}, language = {en} } @article{AbelPikovskij1997, author = {Abel, Markus and Pikovskij, Arkadij}, title = {Parametric excitation of breathers in a nonlinear lattice}, year = {1997}, abstract = {We investigate localized periodic solutions (breathers) in a lattice of parametrically driven, nonlinear dissipative oscillators. These breathers are demonstrated to be exponentially localized, with two characteristic localization lengths. The crossover between the two lengths is shown to be related to the transition in the phase of the lattice oscillations.}, language = {en} } @article{AhlersPikovskij2002, author = {Ahlers, Volker and Pikovskij, Arkadij}, title = {Critical Properties of the Synchronization Transition in Space-Time Chaos}, year = {2002}, abstract = {We study two coupled spatially extended dynamical systems which exhibit space-time chaos. The transition to the synchronized state is treated as a nonequilibrium phase transition, where the average synchronization error is the order parameter. The transition in one-dimensional systems is found to be generically in the universality class of the Kardar- Parisi-Zhang equation with a growth-limiting term ("bounded KPZ"). For systems with very strong nonlinearities in the local dynamics, however, the transition is found to be in the universality class of directed percolation.}, language = {en} } @article{AhlersZillmerPikovskij2001, author = {Ahlers, Volker and Zillmer, R{\"u}diger and Pikovskij, Arkadij}, title = {Lyapunov exponents in disordered chaotic systems : avoided crossing and level statistics}, year = {2001}, abstract = {The behavior of the Lyapunov exponents (LEs) of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, qualitatively similar to the behavior of energy levels in quantum chaos. Recent results for the coupling dependence of the LEs of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small values. The results are interpreted in terms of the random matrix theory.}, language = {en} } @article{AhlersZillmerPikovskij2000, author = {Ahlers, Volker and Zillmer, R{\"u}diger and Pikovskij, Arkadij}, title = {Statistical theory for the coupling sensitivity of chaos}, isbn = {1-563-96915-7}, year = {2000}, language = {en} } @article{AhnertPikovskij2009, author = {Ahnert, Karsten and Pikovskij, Arkadij}, title = {Compactons and chaos in strongly nonlinear lattices}, issn = {1539-3755}, doi = {10.1103/Physreve.79.026209}, year = {2009}, abstract = {We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy.}, language = {en} } @article{AransonPikovskij2022, author = {Aranson, Igor S. and Pikovskij, Arkadij}, title = {Confinement and collective escape of active particles}, series = {Physical review letters}, volume = {128}, journal = {Physical review letters}, number = {10}, publisher = {American Physical Society}, address = {College Park, Md.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.128.108001}, pages = {6}, year = {2022}, abstract = {Active matter broadly covers the dynamics of self-propelled particles. While the onset of collective behavior in homogenous active systems is relatively well understood, the effect of inhomogeneities such as obstacles and traps lacks overall clarity. Here, we study how interacting, self-propelled particles become trapped and released from a trap. We have found that captured particles aggregate into an orbiting condensate with a crystalline structure. As more particles are added, the trapped condensates escape as a whole. Our results shed light on the effects of confinement and quenched disorder in active matter.}, language = {en} } @article{BaibolatovRosenblumZhanabaevetal.2009, author = {Baibolatov, Yernur and Rosenblum, Michael and Zhanabaev, Zeinulla Zh. and Kyzgarina, Meyramgul and Pikovskij, Arkadij}, title = {Periodically forced ensemble of nonlinearly coupled oscillators : from partial to full synchrony}, issn = {1539-3755}, doi = {10.1103/PhysRevE.80.046211}, year = {2009}, abstract = {We analyze the dynamics of a periodically forced oscillator ensemble with global nonlinear coupling. Without forcing, the system exhibits complicated collective dynamics, even for the simplest case of identical phase oscillators: due to nonlinearity, the synchronous state becomes unstable for certain values of the coupling parameter, and the system settles at the border between synchrony and asynchrony, what can be denoted as partial synchrony. We find that an external common forcing can result in two synchronous states: (i) a weak forcing entrains only the mean field, whereas the individual oscillators remain unlocked to the force and, correspondingly, to the mean field; (ii) a strong forcing fully synchronizes the system, making the phases of all oscillators identical. Analytical results are confirmed by numerics.}, language = {en} } @article{BaibolatovRosenblumZhanabaevetal.2010, author = {Baibolatov, Yernur and Rosenblum, Michael and Zhanabaev, Zeinulla Zh. and Pikovskij, Arkadij}, title = {Complex dynamics of an oscillator ensemble with uniformly distributed natural frequencies and global nonlinear coupling}, issn = {1539-3755}, doi = {10.1103/Physreve.82.016212}, year = {2010}, abstract = {We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically (i) states of complete synchrony, (ii) regimes with coexistence of a synchronous cluster and a drifting subpopulation, and (iii) self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.}, language = {en} }