TY - JOUR A1 - Huppert, Amit A1 - Blasius, Bernd A1 - Olinky, Ronen A1 - Stone, Lewi T1 - A Model for Seasonal Phytoplankton Blooms N2 - 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. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/jtb2.pdf ER - TY - JOUR A1 - Blasius, Bernd T1 - Anomalous phase synchronization in two asymmetrically coupled oscillators in the presence of noise N2 - 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 Y1 - 2005 ER - TY - JOUR A1 - Belykh, Vladimir N. A1 - Osipov, Grigory V. A1 - Kuckländer, Nina A1 - Blasius, Bernd A1 - Kurths, Jürgen T1 - Automatic control of phase synchronization in coupled complex oscillators N2 - 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. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/physica_D.pdf ER - TY - JOUR A1 - Blasius, Bernd A1 - Clodong, Sébastien T1 - Chaos in a periodically forced chemostat with algal mortality N2 - 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. Y1 - 2004 ER - TY - JOUR A1 - Fussmann, Gregor F. A1 - Blasius, Bernd T1 - Community response to enrichment is highly sensitive to model structure N2 - 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. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/BiolLett1.pdf ER - TY - JOUR A1 - Bragard, Jean A1 - Montbrio, Ernest A1 - Mendoza, C. A1 - Boccaletti, Stefano A1 - Blasius, Bernd T1 - Defect-enhanced anomaly in frequency synchronization of asymmetrically coupled spatially extended systems N2 - 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. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/pre4.pdf ER - TY - JOUR A1 - Gross, Thilo A1 - D'Lima, Carlos J. Dommar A1 - Blasius, Bernd T1 - Epidemic dynamics on an adaptive network N2 - 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 Y1 - 2006 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.96.208701 SN - 0031-9007 ER - TY - JOUR A1 - Dana, Syamal Kumar A1 - Blasius, Bernd A1 - Kurths, Jürgen T1 - Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators N2 - 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 Y1 - 2006 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.2197168 SN - 1054-1500 ER - TY - JOUR A1 - Wichmann, Matthias A1 - Johst, Karin A1 - Schwager, Monika A1 - Jeltsch, Florian A1 - Blasius, Bernd T1 - Extinction risk, coloured noise and the scaling of variance N2 - 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. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/tpb1.pdf ER - TY - JOUR A1 - Pasternak, Zohar A1 - Blasius, Bernd A1 - Abelson, Avigdor T1 - Host location by larvae of a parasitic barnacle: larval chemotaxis and plume tracking in flow N2 - Numerous studies describe stimulation and/or enhancement of larval settlement by distance chemoreception in response to chemical factors emitted by conspecific adults, host and prey species and microbial films. However, active upstream tracking of odor plumes, needed in order to locate specific, spatially limited settlement sites, has thus far recieved little scientific attention. This study examines host location in flow and still water by larvae of the parasitic barnacle Heterosaccus dollfusi, which inhabits the brachyuran crab Charybdis longicollis. Experiments included analysis of larval motion patterns under four conditions: still water, in flow, in still water with waterborn host metabolites and in flow with host metabolites. Our results show that the H. dollfusi larvae are capable of actively and effectively locating their host in still water and in flow, using chemotaxis and rheotaxis and modifying their swimming pattern, direction, velocity, determination and turning rate to accommodate efficient navigation in changing environmental conditions. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/JPlankR1.pdf ER - TY - JOUR A1 - Pasternak, Zohar A1 - Blasius, Bernd A1 - Abelson, Avigdor A1 - Achituv, Yair T1 - Host-finding behaviour and navigation capabilities of symbiotic zooxanthellae N2 - 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 Y1 - 2006 UR - http://www.springerlink.com/content/100407 U6 - https://doi.org/10.1007/s00338-005-0085-2 ER - TY - JOUR A1 - Pasternak, Zohar A1 - Blasius, Bernd A1 - Abelson, Avigdor A1 - Achituv, Yair T1 - Host-location in flow by larvae of the symbiotic barnacle Savignium dentatum using odor-gated rheotaxis N2 - The detection and location of specific organisms in the aquatic environment, whether they are mates, prey or settlement sites, are two of the most important challenges facing aquatic animals. Large marine invertebrates such as a lobster have been found to locate specific organisms by navigating in the plume of chemicals emitted by the target. However, active plume tracking in flow by small organisms such as a marine larvae has recieved little scientific attention. Here, we present results from a study examining host location in flow by nauplius larvae of the barnacle Trevathana dentata, which inhabits the stony reef coral Cyphastrea chalcidicium.The experiments included analysis of larval motion in an annular flume under four conditions: (i) still water, (ii) in flow, (iii) in still water with waterborne host metabolites and (iv) in flow with host metabolites. Our results show that T. dentata nauplii are unable to locate their target organism in still water using chemotaxis, but are capable of efficient host location in flow using odour-gated rheotaxis. This technique may enable host location by earlier, less-developed larval stages. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/ProcRoySoc4.pdf ER - TY - JOUR A1 - Blasius, Bernd A1 - Rudolf, Lars A1 - Weithoff, Guntram A1 - Gaedke, Ursula A1 - Fussmann, Gregor F. T1 - Long-term cyclic persistence in an experimental predator-prey system JF - Nature : the international weekly journal of science N2 - Predator-prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey(1-4). However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Field observations have been restricted to a few cycle periods(5-8) and experimental studies indicate that oscillations may be short-lived without external stabilizing factors(9-19). Here we performed microcosm experiments with a planktonic predator-prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator-prey phase difference. Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. However, the predator-prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events. Y1 - 2019 U6 - https://doi.org/10.1038/s41586-019-1857-0 SN - 0028-0836 SN - 1476-4687 VL - 577 IS - 7789 SP - 226 EP - 230 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Toenjes, Ralf A1 - Blasius, Bernd T1 - Perturbation analysis of complete synchronization in networks of phase oscillators N2 - The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first- and second-order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erdoumls-Reacutenyi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.80.026202 SN - 1539-3755 ER - TY - JOUR A1 - Toenjes, Ralf A1 - Blasius, Bernd T1 - Perturbation analysis of the Kuramoto phase-diffusion equation subject to quenched frequency disorder N2 - The Kuramoto phase-diffusion equation is a nonlinear partial differential equation which describes the spatiotemporal evolution of a phase variable in an oscillatory reaction-diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in the form of dispersion leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second-order perturbation terms. We apply the theory to simple topologies, like a line or sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter, the synchronized state may become quasidegenerate. We demonstrate how perturbation theory fails at such a critical point. Y1 - 2009 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.79.016112 SN - 1539-3755 ER - TY - JOUR A1 - Blasius, Bernd A1 - Toenjes, Ralf T1 - Quasiregular concentric waves in heterogeneous lattices of coupled oscillators N2 - 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. Y1 - 2005 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/prl1.pdf ER - TY - JOUR A1 - Steuer, Ralf A1 - Gross, Thilo A1 - Selbig, Joachim A1 - Blasius, Bernd T1 - Structural kinetic modeling of metabolic networks JF - Proceedings of the National Academy of Sciences of the United States of America N2 - To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle. KW - systems biology KW - computational biochemistry KW - metabolomics KW - metabolic regulation KW - biological robustness Y1 - 2006 U6 - https://doi.org/10.1073/pnas.0600013103 SN - 0027-8424 SN - 1091-6490 VL - 103 IS - 32 SP - 11868 EP - 11873 PB - National Academy of Sciences CY - Washington ER - TY - JOUR A1 - Montbrio, Ernest A1 - Kurths, Jürgen A1 - Blasius, Bernd T1 - Synchronization of two interacting populations of oscillators N2 - We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators. It includes three types of bistabilities, higher order entrainment and the existence of states with unusual stability properties. All possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically. The impact of these findings for neuroscience is discussed. Y1 - 2004 UR - http://www.agnld.uni-potsdam.de/~bernd/papers/pre3.pdf ER - TY - JOUR A1 - Huppert, Amit A1 - Blasius, Bernd A1 - Stone, Lewi T1 - What minimal models can tell : a reply to van Nes and Scheffer Y1 - 2004 ER - TY - JOUR A1 - Blasius, Bernd A1 - Toenjes, Ralf T1 - Zipf's Law in the popularity distribution of chess openings N2 - We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power law with an exponent that increases linearly with the game depth, whereas the pooled distribution of all opening weights follows Zipf's law with universal exponent. We propose a simple stochastic process that is able to capture the observed playing statistics and show that the Zipf law arises from the self-similar nature of the game tree of chess. Thus, in the case of hierarchical fragmentation the scaling is truly universal and independent of a particular generating mechanism. Our findings are of relevance in general processes with composite decisions. Y1 - 2009 UR - http://prl.aps.org/ U6 - https://doi.org/10.1103/Physrevlett.103.218701 SN - 0031-9007 ER -