@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{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{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{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} } @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{MassieRyabovBlasiusetal.2013, author = {Massie, Thomas Michael and Ryabov, Alexei and Blasius, Bernd and Weithoff, Guntram and Gaedke, Ursula}, title = {Complex transient dynamics of stage-structured populations in response to environmental changes}, series = {The American naturalist : a bi-monthly journal devoted to the advancement and correlation of the biological sciences}, volume = {182}, journal = {The American naturalist : a bi-monthly journal devoted to the advancement and correlation of the biological sciences}, number = {1}, publisher = {Univ. of Chicago Press}, address = {Chicago}, issn = {0003-0147}, doi = {10.1086/670590}, pages = {103 -- 119}, year = {2013}, abstract = {Stage structures of populations can have a profound influence on their dynamics. However, not much is known about the transient dynamics that follow a disturbance in such systems. Here we combined chemostat experiments with dynamical modeling to study the response of the phytoplankton species Chlorella vulgaris to press perturbations. From an initially stable steady state, we altered either the concentration or dilution rate of a growth-limiting resource. This disturbance induced a complex transient response-characterized by the possible onset of oscillations-before population numbers relaxed to a new steady state. Thus, cell numbers could initially change in the opposite direction of the long-term change. We present quantitative indexes to characterize the transients and to show that the dynamic response is dependent on the degree of synchronization among life stages, which itself depends on the state of the population before perturbation. That is, we show how identical future steady states can be approached via different transients depending on the initial population structure. Our experimental results are supported by a size-structured model that accounts for interplay between cell-cycle and population-level processes and that includes resource-dependent variability in cell size. Our results should be relevant to other populations with a stage structure including organisms of higher order.}, 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{MassieWeithoffKucklaenderetal.2015, author = {Massie, Thomas Michael and Weithoff, Guntram and Kucklaender, Nina and Gaedke, Ursula and Blasius, Bernd}, title = {Enhanced Moran effect by spatial variation in environmental autocorrelation}, series = {Nature Communications}, volume = {6}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/ncomms6993}, pages = {8}, year = {2015}, abstract = {Spatial correlations in environmental stochasticity can synchronize populations over wide areas, a phenomenon known as the Moran effect. The Moran effect has been confirmed in field, laboratory and theoretical investigations. Little is known, however, about the Moran effect in a common ecological case, when environmental variation is temporally autocorrelated and this autocorrelation varies spatially. Here we perform chemostat experiments to investigate the temporal response of independent phytoplankton populations to autocorrelated stochastic forcing. In contrast to naive expectation, two populations without direct coupling can be more strongly correlated than their environmental forcing (enhanced Moran effect), if the stochastic variations differ in their autocorrelation. Our experimental findings are in agreement with numerical simulations and analytical calculations. The enhanced Moran effect is robust to changes in population dynamics, noise spectra and different measures of correlation-suggesting that noise-induced synchrony may play a larger role for population dynamics than previously thought.}, 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{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} }