@article{ZaikinKurths2006, author = {Zaikin, Alexey and Kurths, J{\"u}rgen}, title = {Optimal length transportation hypothesis to model proteasome product size distribution}, series = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences}, volume = {32}, journal = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences}, number = {3-4}, publisher = {Springer}, address = {Dordrecht}, issn = {0092-0606}, doi = {10.1007/s10867-006-9014-z}, pages = {231 -- 243}, year = {2006}, abstract = {This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.}, language = {en} } @article{MeucciSalvadoriIvanchenkoetal.2006, author = {Meucci, Riccardo and Salvadori, Francesco and Ivanchenko, Mikhail V. and Al Naimee, Kais and Zhou, Chansong and Arecchi, Fortunato Tito and Boccaletti, Stefano and Kurths, J{\"u}rgen}, title = {Synchronization of spontaneous bursting in a CO2 laser}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {74}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.74.066207}, pages = {6}, year = {2006}, abstract = {We present experimental and numerical evidence of synchronization of burst events in two different modulated CO2 lasers. Bursts appear randomly in each laser as trains of large amplitude spikes intercalated by a small amplitude chaotic regime. Experimental data and model show the frequency locking of bursts in a suitable interval of coupling strength. We explain the mechanism of this phenomenon and demonstrate the inhibitory properties of the implemented coupling.}, language = {en} } @article{ZemanovaZhouKurths2006, author = {Zemanova, Lucia and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Structural and functional clusters of complex brain networks}, series = {Physica, D, Nonlinear phenomena}, volume = {224}, journal = {Physica, D, Nonlinear phenomena}, number = {1-2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2006.09.008}, pages = {202 -- 212}, year = {2006}, abstract = {Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.}, language = {en} } @article{ZouThielRomanoetal.2006, author = {Zou, Yong and Thiel, M. and Romano, Maria Carmen and Kurths, J{\"u}rgen and Bi, Q.}, title = {Shrimp structure and associated dynamics in parametrically excited oscillators}, series = {International journal of bifurcation and chaos : in applied sciences and engineering}, volume = {16}, journal = {International journal of bifurcation and chaos : in applied sciences and engineering}, number = {12}, publisher = {World Scientific Publ. Co}, address = {Singapore}, issn = {0218-1274}, doi = {10.1142/S0218127406016987}, pages = {3567 -- 3579}, year = {2006}, abstract = {We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system.}, language = {en} } @article{ZhouZemanovaZamoraetal.2006, author = {Zhou, Changsong and Zemanova, Lucia and Zamora, Gorka and Hilgetag, Claus C. and Kurths, J{\"u}rgen}, title = {Hierarchical organization unveiled by functional connectivity in complex brain networks}, series = {Physical review letters}, volume = {97}, journal = {Physical review letters}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.97.238103}, pages = {4}, year = {2006}, abstract = {How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.}, language = {en} } @article{GandhimathiRajasekarKurths2006, author = {Gandhimathi, V. M. and Rajasekar, S. and Kurths, J{\"u}rgen}, title = {Vibrational and stochastic resonances in two coupled overdamped anharmonic oscillators}, series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, volume = {360}, journal = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, number = {2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0375-9601}, doi = {10.1016/j.physleta.2006.08.051}, pages = {279 -- 286}, year = {2006}, abstract = {We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved.}, language = {en} } @article{RomanoThielKurthsetal.2006, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Rolfs, Martin and Engbert, Ralf and Kliegl, Reinhold}, title = {Synchronization Analysis and Recurrence in Complex Systems}, isbn = {978-3-527-40623-4}, year = {2006}, language = {en} } @article{ZhouKurths2006, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Hierarchical synchronization in complex networks with heterogeneous degrees}, issn = {1054-1500}, doi = {10.1063/1.2150381}, year = {2006}, abstract = {We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics}, language = {en} } @article{ZhouMotterKurths2006, author = {Zhou, Changsong and Motter, Adilson E. and Kurths, J{\"u}rgen}, title = {Universality in the synchronization of weighted random networks}, doi = {10.1103/Physrevlett.96.034101}, year = {2006}, abstract = {Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters}, language = {en} } @article{ZhouKurths2006, author = {Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Dynamical weights and enhanced synchronization in adaptive complex networks}, doi = {10.1103/Physrevlett.96.164102}, year = {2006}, abstract = {Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks}, language = {en} } @article{ThielRomanoKurthsetal.2006, author = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold}, title = {Twin surrogates to test for complex synchronisation}, doi = {10.1209/epl/i2006-10147-0}, year = {2006}, abstract = {We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems}, language = {en} } @article{SchelterWinterhalderDahlhausetal.2006, author = {Schelter, Bj{\"o}rn and Winterhalder, Matthias and Dahlhaus, Rainer and Kurths, J{\"u}rgen and Timmer, Jens}, title = {Partial phase synchronization for multivariate synchronizing systems}, doi = {10.1103/Physrevlett.96.208103}, year = {2006}, abstract = {Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated}, language = {en} } @article{LandaUshakovKurths2006, author = {Landa, Polina S. and Ushakov, Vladimir and Kurths, J{\"u}rgen}, title = {Rigorous theory of stochastic resonance in overdamped bistable oscillators for weak signals}, series = {Chaos, solitons \& fractals : applications in science and engineering}, volume = {30}, journal = {Chaos, solitons \& fractals : applications in science and engineering}, number = {3}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0960-0779}, doi = {10.1016/j.chaos.2005.08.116}, pages = {574 -- 578}, year = {2006}, abstract = {The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.}, language = {en} } @article{GozolchianiMoshelHausdorffetal.2006, author = {Gozolchiani, Avi and Moshel, Shay and Hausdorff, Jeffrey M. and Simon, Ely and Kurths, J{\"u}rgen and Havlin, Shlomo}, title = {Decaying of phase synchronization in parkinsonian tremor}, issn = {0378-4371}, doi = {10.1016/j.physa.2005.10.033}, year = {2006}, abstract = {We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.}, language = {en} } @article{BaptistaZhouKurths2006, author = {Baptista, Murilo da Silva and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Information transmission in phase synchronous chaotic arrays}, issn = {0256-307X}, doi = {10.1088/0256-307X/23/3/010}, year = {2006}, abstract = {We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize}, language = {en} } @article{PereiraBaptistaReyesetal.2006, author = {Pereira, Tiago and Baptista, Murilo da Silva and Reyes, Marcelo Bussotti and Caldas, Ibere Luiz and Sartorelli, Jos{\´e} Carlos and Kurths, J{\"u}rgen}, title = {Global bifurcation destroying the experimental torus T-2}, doi = {10.1103/Physreve.73.017201}, year = {2006}, abstract = {We show experimentally the scenario of a two-frequency torus T-2 breakdown, in which a global bifurcation occurs due to the collision of a torus with an unstable periodic orbit, creating a heteroclinic saddle connection, followed by an intermittent behavior}, language = {en} } @article{BaptistaPereiraKurths2006, author = {Baptista, Murilo da Silva and Pereira, Tiago and Kurths, J{\"u}rgen}, title = {Upper bounds in phase synchronous weak coherent chaotic attractors}, issn = {0167-2789}, doi = {10.1016/j.physd.2006.02.007}, year = {2006}, abstract = {An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.}, language = {en} } @article{LiSunKurths2006, author = {Li, Changpin and Sun, Weigang and Kurths, J{\"u}rgen}, title = {Synchronization of complex dynamical networks with time delays}, issn = {0378-4371}, doi = {10.1016/j.physa.2005.07.007}, year = {2006}, abstract = {In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.}, language = {en} } @article{ThielRomanoKurths2006, author = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen}, title = {Spurious structures in recurrence plots induced by embedding}, doi = {10.1007/s11071-006-2010-9}, year = {2006}, abstract = {In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay}, language = {en} } @article{BoccalettiHwangChavezetal.2006, author = {Boccaletti, Stefano and Hwang, Dong-Uk and Chavez, Mario and Amann, Andreas and Kurths, J{\"u}rgen and Pecora, Louis M.}, title = {Synchronization in dynamical networks : evolution along commutative graphs}, issn = {1539-3755}, doi = {10.1103/Physreve.74.016102}, year = {2006}, abstract = {Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior}, language = {en} } @article{AnishchenkoNikolaevKurths2006, author = {Anishchenko, Vadim S. and Nikolaev, S and Kurths, J{\"u}rgen}, title = {Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions}, issn = {1539-3755}, doi = {10.1103/Physreve.73.056202}, year = {2006}, abstract = {We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place}, language = {en} } @article{RaabWesselSchirdewanetal.2006, author = {Raab, Corinna and Wessel, Niels and Schirdewan, Alexander and Kurths, J{\"u}rgen}, title = {Large-scale dimension densities for heart rate variability analysis}, issn = {1539-3755}, doi = {10.1103/Physreve.73.041907}, year = {2006}, abstract = {In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification}, language = {en} } @article{DanaBlasiusKurths2006, author = {Dana, Syamal Kumar and Blasius, Bernd and Kurths, J{\"u}rgen}, title = {Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators}, issn = {1054-1500}, doi = {10.1063/1.2197168}, year = {2006}, abstract = {We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models}, language = {en} } @article{VasconcelosLopesVianaetal.2006, author = {Vasconcelos, D. B. and Lopes, S. R. and Viana, R. L. and Kurths, J{\"u}rgen}, title = {Spatial recurrence plots}, doi = {10.1103/Physreve.73.056207}, year = {2006}, abstract = {We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes}, language = {en} } @article{KurthsRomanoThieletal.2006, author = {Kurths, J{\"u}rgen and Romano, Maria Carmen and Thiel, Marco and Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kiss, Istvan Z. and Hudson, John L.}, title = {Synchronization analysis of coupled noncoherent oscillators}, issn = {0924-090X}, doi = {10.1007/s11071-006-1957-x}, year = {2006}, abstract = {We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators}, language = {en} } @article{WinterhalderSchelterKurthsetal.2006, author = {Winterhalder, Matthias and Schelter, B and Kurths, J{\"u}rgen and Schulze-Borthage, A and Timmer, Jens}, title = {Sensitivity and specificity of coherence and phase synchronization analysis}, doi = {10.1016/j.physleta.2006.03.018}, year = {2006}, abstract = {In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved}, language = {en} }