@article{BelykhOsipovKucklaenderetal.2005,
  author    = {Belykh, Vladimir N. and Osipov, Grigory V. and Kuckl{\"a}nder, Nina and Blasius, Bernd and Kurths, J{\"u}rgen},
  title     = {Automatic control of phase synchronization in coupled complex oscillators},
  year      = {2005},
  abstract  = {We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic R"ossler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic R"ossler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.},
  language  = {en}
}
@article{Blasius2005,
  author    = {Blasius, Bernd},
  title     = {Anomalous phase synchronization in two asymmetrically coupled oscillators in the presence of noise},
  year      = {2005},
  abstract  = {We study the route to synchronization in two noisy, nonisochronous oscillators. Anomalous phase synchronization arises if both oscillators differ in their respective value of nonisochronicity and it is characterized by a strong detuning of the oscillator frequencies with the onset of coupling. Here we show that anomalous synchronization, both in limit-cycle or chaotic oscillators, can considerably be enlarged under the influence of asymmetrical coupling and noise. In these systems we describe a number of noise induced effects, such as an inversion of the natural frequency difference and coupling induced desynchronization of two identical oscillators. Our results can be explained in terms of a noisy particle in a tilted washboard potential},
  language  = {en}
}
@article{BlasiusToenjes2005,
  author    = {Blasius, Bernd and Toenjes, Ralf},
  title     = {Quasiregular concentric waves in heterogeneous lattices of coupled oscillators},
  year      = {2005},
  abstract  = {We study the pattern formation in a lattice of locally coupled phase oscillators with quenched disorder. In the synchronized regime quasi regular concentric waves can arise which are induced by the disorder of the system. Maximal regularity is found at the edge of the synchronization regime. The emergence of the concentric waves is related to the symmetry breaking of the interaction function. An explanation of the numerically observed phenomena is given in a one- dimensional chain of coupled phase oscillators. Scaling properties, describing the target patterns are obtained.},
  language  = {en}
}
@article{BragardMontbrioMendozaetal.2005,
  author    = {Bragard, Jean and Montbrio, Ernest and Mendoza, C. and Boccaletti, Stefano and Blasius, Bernd},
  title     = {Defect-enhanced anomaly in frequency synchronization of asymmetrically coupled spatially extended systems},
  year      = {2005},
  abstract  = {We analytically establish and numerically show that anomalous frequency synchronization occurs in a pair of asymmetrically coupled chaotic space extended oscillators. The transition to anomalous behaviors is crucially dependent on asymmetries in the coupling configuration, while the presence of phase defects has the effect of enhancing the anomaly in frequency synchronization with respect to the case of merely time chaotic oscillators.},
  language  = {en}
}
@article{FussmannBlasius2005,
  author    = {Fussmann, Gregor F. and Blasius, Bernd},
  title     = {Community response to enrichment is highly sensitive to model structure},
  year      = {2005},
  abstract  = {Biologists use mathematical functions to model, understand, and predict nature. For most biological processes, however, the exact analytical form is not known. This is also true for one of the most basic life processes, the uptake of food or resources. We show that the use of a number of nearly indistinguishable functions, which can serve as phenomenological descriptors of resource uptake, may lead to alarmingly different dynamical behaviour in a simple community model. More specifically, we demonstrate that the degree of resource enrichment needed to destabilize the community dynamics depends critically on the mathematical nature of the uptake function.},
  language  = {en}
}
@article{HuppertBlasiusOlinkyetal.2005,
  author    = {Huppert, Amit and Blasius, Bernd and Olinky, Ronen and Stone, Lewi},
  title     = {A Model for Seasonal Phytoplankton Blooms},
  year      = {2005},
  abstract  = {We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time series. Instead the model has a tendency to `skip' with outbreaks often being suppressed from one year to the next. This behaviour is studied in detail and we develop an analytical expression to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics.},
  language  = {en}
}
@article{WichmannJohstSchwageretal.2005,
  author    = {Wichmann, Matthias and Johst, Karin and Schwager, Monika and Jeltsch, Florian and Blasius, Bernd},
  title     = {Extinction risk, coloured noise and the scaling of variance},
  year      = {2005},
  abstract  = {The impact of temporally correlated fluctuating environments (coloured noise) on the extinction risk of populations has become a main focus in theoretical population ecology. In this study we particularly focus on the extinction risk in strongly autocorrelated environments. Here, in contrast to moderate autocorrelation, we found the extinction risk to be highly dependent on the process of noise generation, in particular on the method of variance scaling. Such variance scaling is commonly applied to avoid variance-driven biases when comparing the extinction risk for white and coloured noise. In this study we found an often-used scaling technique to lead to high variability in the resulting variances of different time series for strong auto-correlation eventually leading to deviations in the projected extinction risk. Therefore, we present an alternative method that always delivers the target variance, even in the case of strong temporal correlation. Furthermore, in contrast to the earlier method, our very intuitive method is not bound to auto-regressive processes but can be applied to all types of coloured noises. We recommend the method introduced here to be used when the target of interest is the effect of noise colour on extinction risk not obscured by any variance effects.},
  language  = {en}
}