@article{IvanchenkoOsipovShalfeevetal.2004,
  author    = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen},
  title     = {Synchronization of two non-scalar-coupled limit-cycle oscillators},
  year      = {2004},
  abstract  = {Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{OsipovIvanchenkoKurthsetal.2005,
  author    = {Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kurths, J{\"u}rgen and Hu, B.},
  title     = {Synchronized chaotic intermittent and spiking behavior in coupled map chains},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks},
  language  = {en}
}
@article{KitajimaKurths2005,
  author    = {Kitajima, H. and Kurths, J{\"u}rgen},
  title     = {Synchronized firing of FitzHugh-Nagumo neurons by noise},
  issn      = {1054-1500},
  year      = {2005},
  abstract  = {We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. (C) 2005 American Institute of Physics},
  language  = {en}
}
@article{KoseskaVolkovKurths2011,
  author    = {Koseska, Aneta and Volkov, Evgenii and Kurths, J{\"u}rgen},
  title     = {Synthetic multicellular oscillatory systems controlling protein dynamics with genetic circuits},
  series = {Physica scripta : an international journal for experimental and theoretical physics},
  volume    = {84},
  journal   = {Physica scripta : an international journal for experimental and theoretical physics},
  number    = {4},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0031-8949},
  doi       = {10.1088/0031-8949/84/04/045007},
  pages     = {10},
  year      = {2011},
  abstract  = {Synthetic biology is a relatively new research discipline that combines standard biology approaches with the constructive nature of engineering. Thus, recent efforts in the field of synthetic biology have given a perspective to consider cells as 'programmable matter'. Here, we address the possibility of using synthetic circuits to control protein dynamics. In particular, we show how intercellular communication and stochasticity can be used to manipulate the dynamical behavior of a population of coupled synthetic units and, in this manner, finely tune the expression of specific proteins of interest, e.g. in large bioreactors.},
  language  = {en}
}
@unpublished{EngbertScheffczykKrampeetal.1997,
  author    = {Engbert, Ralf and Scheffczyk, Christian and Krampe, Ralf-Thomas and Rosenblum, Mikhael and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Tempo-induced transitions in polyrhythmic hand movements},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14380},
  year      = {1997},
  abstract  = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.},
  language  = {en}
}
@article{ScheffczykKrampeEngbertetal.1997,
  author    = {Scheffczyk, Christian and Krampe, Ralf-Thomas and Engbert, Ralf and Rosenblum, Michael and Kurths, J{\"u}rgen and Kliegl, Reinhold},
  title     = {Tempo-induced transitions in polyrhythmic hand movements},
  year      = {1997},
  abstract  = {We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.},
  language  = {en}
}
@article{VossKurths1998,
  author    = {Voss, Henning U. and Kurths, J{\"u}rgen},
  title     = {Test for nonlinear dynamical behavior in symbol sequences},
  year      = {1998},
  language  = {en}
}
@article{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {Testing for phase synchronization},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-sample test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series},
  language  = {en}
}
@misc{AllefeldKurths2004,
  author    = {Allefeld, Carsten and Kurths, J{\"u}rgen},
  title     = {Testing for phase synchronization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-20091},
  year      = {2004},
  abstract  = {We present different tests for phase synchronization which improve the procedures currently used in the literature. This is accomplished by using a two-samples test setup and by utilizing insights and methods from directional statistics and bootstrap theory. The tests differ in the generality of the situation in which they can be applied as well as in their complexity, including computational cost. A modification of the resampling technique of the bootstrap is introduced, making it possible to fully utilize data from time series.},
  language  = {en}
}
@article{EngbertHainzlZoelleretal.1998,
  author    = {Engbert, Ralf and Hainzl, Sebastian and Z{\"o}ller, Gert and Kurths, J{\"u}rgen},
  title     = {Testing for unstable periodic orbits to characterize spatiotemporal dynamics},
  year      = {1998},
  language  = {en}
}
@article{WittKurthsPikovskij1998,
  author    = {Witt, Annette and Kurths, J{\"u}rgen and Pikovskij, Arkadij},
  title     = {Testing stationarity in time series},
  year      = {1998},
  language  = {en}
}
@article{ZiehmannSmithKurths1999,
  author    = {Ziehmann, Christine and Smith, L. and Kurths, J{\"u}rgen},
  title     = {The bootstrap and lyapunov exponents in deterministic chaos},
  year      = {1999},
  language  = {en}
}
@article{PalusKurthsSchwarzetal.2007,
  author    = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Seehafer, Norbert and Novotna, Dagmar and Charvatova, Ivanka},
  title     = {The solar activity cycle is weakly synchronized with the solar inertial motion},
  doi       = {10.1016/j.physleta.2007.01.039},
  year      = {2007},
  abstract  = {We study possible interrelations between the 300-year record of the yearly sunspot numbers and the solar inertial motion (SIM) using the recently developed technique of synchronization analysis. Phase synchronization of the sunspot cycle and the SIM is found and statistically confirmed in three epochs (1734-1790, 1855-1875 and 1907-1960) of the whole period 1700-2000. These results give quantitative support to the hypothesis that there is a weak interaction between the solar activity and the SIM.},
  language  = {en}
}
@article{BoccalettiKurthsOsipov2002,
  author    = {Boccaletti, Stefano and Kurths, J{\"u}rgen and Osipov, Grigory V.},
  title     = {The synchronization of chaotic systems},
  year      = {2002},
  language  = {en}
}
@misc{KoseskaZaikinKurthsetal.2009,
  author    = {Koseska, Aneta and Zaikin, Alexey and Kurths, J{\"u}rgen and Garc{\´i}a-Ojalvo, Jordi},
  title     = {Timing cellular decision making under noise via cell-cell communication},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-45260},
  year      = {2009},
  abstract  = {Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact.},
  language  = {en}
}
@article{StolbovaSurovyatkinaBookhagenetal.2016,
  author    = {Stolbova, Veronika and Surovyatkina, Elena and Bookhagen, Bodo and Kurths, J{\"u}rgen},
  title     = {Tipping elements of the Indian monsoon: Prediction of onset and withdrawal},
  series = {Geophysical research letters},
  volume    = {43},
  journal   = {Geophysical research letters},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {0094-8276},
  doi       = {10.1002/2016GL068392},
  pages     = {3982 -- 3990},
  year      = {2016},
  abstract  = {Forecasting the onset and withdrawal of the Indian summer monsoon is crucial for the life and prosperity of more than one billion inhabitants of the Indian subcontinent. However, accurate prediction of monsoon timing remains a challenge, despite numerous efforts. Here we present a method for prediction of monsoon timing based on a critical transition precursor. We identify geographic regions-tipping elements of the monsoon-and use them as observation locations for predicting onset and withdrawal dates. Unlike most predictability methods, our approach does not rely on precipitation analysis but on air temperature and relative humidity, which are well represented both in models and observations. The proposed method allows to predict onset 2 weeks earlier and withdrawal dates 1.5 months earlier than existing methods. In addition, it enables to correctly forecast monsoon duration for some anomalous years, often associated with El Nino-Southern Oscillation.},
  language  = {en}
}
@article{BraunFeudelGebogietal.1999,
  author    = {Braun, Robert and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Witt, Annette},
  title     = {Tracer dynamics in a flow of driven vortices},
  year      = {1999},
  language  = {en}
}
@article{PopovychMaistrenkoMosekildeetal.2000,
  author    = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Transcritical loss of synchronization in coupled chaotic systems},
  year      = {2000},
  language  = {en}
}
@article{PopovychMaistrenkoMosekildeetal.2001,
  author    = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Transcritical riddling in a system of coupled maps},
  year      = {2001},
  abstract  = {The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.},
  language  = {en}
}
@article{HassanKurths2001,
  author    = {Hassan, M. K. and Kurths, J{\"u}rgen},
  title     = {Transition from random to ordered fractals in fragmentation of particles in an open system},
  year      = {2001},
  language  = {en}
}