@article{PasternakBlasiusAbelsonetal.2006,
  author    = {Pasternak, Zohar and Blasius, Bernd and Abelson, Avigdor and Achituv, Yair},
  title     = {Host-finding behaviour and navigation capabilities of symbiotic zooxanthellae},
  doi       = {10.1007/s00338-005-0085-2},
  year      = {2006},
  abstract  = {Past studies have shown that the initiation of symbiosis between the Red-Sea soft coral Heteroxenia fuscescens and its symbiotic dinoflagellates occurs due to the chemical attraction of the motile algal cells to substances emanating from the coral polyps. However, the resulting swimming patterns of zooxanthellae have not been previously studied. This work examined algal swimming behaviour, host location and navigation capabilities under four conditions: (1) still water, (2) in still water with waterborne host attractants, (3) in flowing water, and (4) in flow with host attractants. Algae were capable of actively and effectively locating their host in still water as well as in flow. When in water containing host attractants, swimming became slower, motion patterns straighter and the direction of motion was mainly towards the host-even if this meant advancing upstream against flow velocities of up to 0.5 mm s(-1)supercript stop. Coral-algae encounter probability decreased the further downstream of the host algae were located, probably due to diffusion of the chemical signal. The results show how the chemoreceptive zooxanthellae modify their swimming pattern, direction, velocity, circuity and turning rate to accommodate efficient navigation in changing environmental conditions},
  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{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{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{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}
}
@article{GrossD'LimaBlasius2006,
  author    = {Gross, Thilo and D'Lima, Carlos J. Dommar and Blasius, Bernd},
  title     = {Epidemic dynamics on an adaptive network},
  issn      = {0031-9007},
  doi       = {10.1103/Physrevlett.96.208701},
  year      = {2006},
  abstract  = {Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications},
  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{BlasiusClodong2004,
  author    = {Blasius, Bernd and Clodong, S{\´e}bastien},
  title     = {Chaos in a periodically forced chemostat with algal mortality},
  year      = {2004},
  abstract  = {We study the possibility of chaotic dynamics in the externally driven Droop model. This model describes a phytoplankton population in a chemostat under periodic supply of nutrients. Previously it has been proven under very general assumptions that such systems are not able to exhibit chaotic dynamics. Here we show that the simple introduction of algal mortality may lead to chaotic oscillations of algal density in the forced chemostat. Our numerical simulations show that the existence of chaos is intimately related to plankton overshooting in the unforced model. We provide a simple measure, based on stability analysis, for estimating the amount of overshooting. These findings are not restricted to the Droop model but hold also for other chemostat models with mortality. Our results suggest periodically driven chemostats as a simple model system for the experimental verification of chaos in ecology.},
  language  = {en}
}