Publications & Talks


Citations on Google Scholar.

Supplementary Informations for Papers here.

In Preparation / under Review

  1. Christian Bick, Mark J. Panaggio, Erik A. Martens
    Chaotic Mean Field Dynamics in Phase Oscillators with Heterogeneous Phase-lag
    (in preparation); arXiv:
    > Abstract
  2. Erik A. Martens and Konstantin Klemm
    Transitions from Trees to Cycles in Adaptive Flow Networks
    (submitted); arXiv:
    > Abstract

Published / in Press

  1. Erik A. Martens, Christian Bick, Mark J. Panaggio
    Chimera States in Two Populations with Heterogeneous Phase-lag
    Chaos 26 (9), 094819 (2016); doi: 10.1063/1.4958930; arXiv:1606.0187
    > Abstract

    The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra- and inter-population coupling strengths. We explore the effects of heterogeneous coupling phase-lags between the two populations. Such heterogeneity arises naturally in various settings, for example as an approximation to transmission delays, excitatory-inhibitory interactions, or as amplitude and phase responses of oscillators with electrical or mechanical coupling. We find that breaking the phase-lag symmetry results in a variety of states with uniform and non-uniform synchronization, including in-phase and anti-phase synchrony, full incoherence (splay state), chimera states with phase separation of 0 or π between populations, and states where both populations remain desynchronized. These desynchronized states exhibit stable, oscillatory, and even chaotic dynamics. Moreover, we identify the bifurcations through which chimera and desynchronized states emerge. Stable chimera states and desynchronized solutions, which do not arise for homogeneous phase-lag parameters, emerge as a result of competition between synchronized in-phase, anti-phase equilibria, and fully incoherent states when the phase-lags are near ±π/2 (cosine coupling). These findings elucidate previous experimental results involving a network of mechanical oscillators and provide further insight into the breakdown of synchrony in biological systems.

  2. D.D. Postnov, D. J. Marsh, D. E. Postnov, T.H. Braunstein, N.H. Holstein-Rathlou, Erik A. Martens, and O. Sosnovtseva.
    Modeling of Kidney Hemodynamics: Probability-Based Topology of an Arterial Network.
    PLoS Computational Bioliogy 12(7): e1004922 (2016). doi:10.1371/journal.pcbi.1004922
    > Abstract

    Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons. The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney. Using these results together with published micro-computed tomography (μCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall. Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons.

  3. Erik A. Martens, Mark Panaggio, Daniel M. Abrams
    Basins of Attraction for Chimera States
    New Journal of Physics, Fast Track Communication, 18:022002 (2016); doi: 10.1088/1367-2630/18/2/022002; arXiv:1507.01457
    Supplementary Videos here.
    > Abstract

    Separatrix around R0
    Chimera states---curious symmetry-broken states in systems of identical coupled oscillators---typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.

  4. Simona Olmi, Erik A. Martens, Shashi Thutupalli, Alessandro Torcini
    Intermittent Chaotic Chimeras for Coupled Rotators
    Phys. Rev. E Rapid Communications, 92, 030901 (R) (2015), doi:10.1103/PhysRevE.92.030901; arXiv:1507.07685

    Intermittent Chaotic Chimera
    Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendula. In particular, we report the first evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite life-times diverging as a power-law with N and m. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.

  5. Erik A. Martens*, Navish Wadhwa*, Nis S. Jacobsen, Christian Lindemann, Ken H. Andersen, and André Visser
    Size Structures Sensory Hierarchy in Ocean Life
    Proceedings of the Royal Society B, 282:20151346 (2015); doi: 10.1101/018937; biorXiv:10.1101/018937

    Life in the ocean is shaped by the trade-off between a need to encounter other organisms for feeding or mating, and to avoid encounters with predators. Avoiding or achieving encounters necessitates an efficient means of collecting the maximum possible information from the surroundings through the use of remote sensing. In this study, we explore how sensing mode and range depend on body size. We reveal a hierarchy of sensing modes (chemosensing, mechanosensing, vision, hearing, and echolocation) where body size determines the available battery of sensing modes and where larger body size means a longer sensing range. The size-dependent hierarchy and the transitions between primary sensory modes are explained on the grounds of limiting factors set by physiology and the physical laws governing signal generation, transmission and reception. We characterize the governing mechanisms and theoretically predict the body size limits for various sensory modes, which align very well with size ranges found in literature. The treatise of all ocean life, from unicellular organisms to whales, demonstrates how body size determines available sensing modes, and thereby acts as a major structuring factor of aquatic life.

    Supplementary Text

  6. K.H. Andersen, T. Berge, R.J. Gonçalves, M. Hartvig, J. Heuschele, S. Hylander,
    N.S. Jacobsen, C.Lindemann, E.A. Martens, A.B. Neuheimer, K. Olsson, A. Palacz,
    F. Prowe, J.Sainmont, S.J. Traving, A.W. Visser, N. Wadhwa and T. Kiørboe

    Characteristic Sizes of Life in the Oceans, from Bacteria to Whales.
    Annual Review of Marine Science 8:3.1–3.25 (2016), doi: 10.1146/annurev-marine-122414-034144

    The size of an individual organism is a key trait to characterize its physiology and feeding ecology. Size-based scaling laws may have a limited size range of validity or undergo a transition from one scaling exponent to another at some characteristic size. We collate and review data on size-based scaling laws for resource acquisition, mobility, sensory range, and progeny size for all pelagic marine life, from bacteria to whales. Further, we review and develop simple theoretical arguments for observed scaling laws and the characteristic sizes of a change or breakdown of power laws. We divide life in the ocean into seven major realms based on trophic strategy, physiology, and life history strategy. Such a categorization represents a move away from a taxonomically oriented description toward a trait-based description of life in the oceans. Finally, we discuss life forms that transgress the simple size-based rules and identify unanswered questions.

  7. Christian Bick and Erik A. Martens
    Controlling Chimeras
    New Journal of Physics 17:033030 (2015), doi:10.1088/1367-2630/17/3/033030; arXiv:1402.6363

    Supplementary Video here.

    Logo_ChimeraControl Coupled phase oscillators model a variety of dynamical phenomena in nature and technological applications. Non-local coupling gives rise to chimera states which are characterized by a distinct part of phase-synchronized oscillators while the remaining ones move incoherently. Here, we apply the idea of control to chimera states: using gradient dynamics to exploit drift of a chimera, it will attain any desired target position. Through control, chimera states become functionally relevant; for example, the controlled position of localized synchrony may encode information and perform computations. Since functional aspects are crucial in (neuro-)biology and technology, the localized synchronization of a chimera state becomes accessible to develop novel applications. Based on gradient dynamics, our control strategy applies to any suitable observable and can be generalized to arbitrary dimensions. Thus, the applicability of chimera control goes beyond chimera states in non-locally coupled systems.

  8. C. Kuehn*, Erik A. Martens*, D. Romero
    Critical Transitions in Social Network Activity
    Journal of Complex Networks 2(2), p.1-12 (2014), doi:10.1093/comnet/cnt022; arXiv:1307.8250
    > Abstract
    Logo_CritialTransitions A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the dynamical state of the system abruptly changes. For example, such critical transitions may result in the sudden change of ecological environments and climate conditions. Data and models suggest that detectable warning signs may precede some of these drastic events. This view is also corroborated by abstract mathematical theory for generic bifurcations in stochastic multi-scale systems. Whether such stochastic scaling laws used as warning signs for apriori unknown events in society are present in social networks is an exciting open problem, to which at present only highly speculative answers can be given. Here, we instead provide a first step towards tackling a simpler question by focusing on a priori known events and analyse a social media data set with a focus on classical variance and autocorrelation warning signs. Our results thus pertain to one absolutely fundamental question: Can the stochastic warning signs known from other areas also be detected in large-scale social media data? We answer this question affirmatively as we find that several apriori known events are preceded by variance and autocorrelation growth. Our findings thus clearly establish the necessary starting point to further investigate the relationship between abstract mathematical theory and various classes of critical transitions in social networks.

    Covered in Oxford University Press Blog, 2014
  9. Erik A. Martens, Shashi Thutupalli, Antoine Fourrière and Oskar Hallatschek
    Chimera States in Mechanical Oscillator Networks
    Proc. Natl. Acad. Sci., Vol. 110 (26), p. 10563–10567 (2013), doi:10.1073/pnas.1302880110; arXiv:1301.7608
    Supplementary informations here and here.

    Logo_PHJ The synchronization of coupled oscillators is a striking manifestation of self-organization that nature employs to orchestrate essential processes of life, such as the beating of the heart. While it was long thought that synchrony or disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies over the last 10 years revealed the intriguing possibility of `chimera states', in which the symmetry of the oscillator population is broken into a synchronous and an asynchronous part. Particularly, numerous analytical studies, involving different network topologies, and various sources of random perturbations establish chimeras as a robust theoretical concept and suggest that they exist in complex systems in nature. Yet, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic to natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behaviour, such as power grids, opto-mechanical crystals or cells communicating via quorum sensing in microbial populations.

    Featured in Physik Journal, "Die Schimäre lebt", by Arkady Pikovsky, Michael Rosenblum and Jürgen Kurths. Issue of September 2013.

    Appeared in Physics Today, Backscatter: "A Mechanical Chimera". Vol. 66, Issue 10 of October 2013.

    FOKOS award for the most surprising/striking discovery reported in 2013 (PDF of Award)

  10. Erik A. Martens, S. Watanabe and T. Bohr
    Model for Polygonal Hydraulic Jumps
    Phys. Rev. E Vol. 85, 036316 (2012); arXiv:1111.4599
    Supplementary informations

    hexagon We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard et al., based on the known flow structure for the type II hydraulic jumps with a "roller" (separation eddy) near the free in the jump region. The model consists of mass conservation and radial force balance between hydrostatic pressure and viscous stresses on the roller surface. In addition, we consider the azimuthal force balance, primarily between pressure and viscosity, but also including non-hydrostatic pressure contributions from surface tension in light of recent observations by Bush et al. The model can be analyzed by linearization around the circular state, resulting in a parameter relationship for nearly circular polygonal states. A truncated, but fully nonlinear version of the model can be solved analytically. This simpler model gives rise to polygonal shapes that are very similar to those observed in experiments, even though surface tension is neglected, and the condition for the existence of a polygon with N corners depends only on a single dimensionless number φ. Finally, we include time-dependent terms in the model and study linear stability of the circular state. Instability occurs for suffciently small Bond number and the most unstable wave length is expected to be roughly proportional to the width of the roller as in the Rayleigh-Plateau instability.

    Highlighted in Physical Review E. Kaleidoscope

    Read Summary Text
  11. Erik A. Martens, R. Kostadinov, C. C. Maley and O. Hallatschek
    Spatial Structure Increases the Waiting for Cancer
    New Journal of Physics 13, 115014 (2011); arXiv:1106.3005
    Focus Issue "Physics of Cancer"

    hexagon Cancer results from a sequence of genetic and epigenetic changes that lead to a variety of abnormal phenotypes including increased proliferation and survival of somatic cells and thus to a selective advantage of pre-cancerous cells. The notion of cancer progression as an evolutionary process has been attracting increasing interest in recent years. A great deal of effort has been made to better understand and predict the progression to cancer using mathematical models; these mostly consider the evolution of a well-mixed cell population, even though pre-cancerous cells often evolve in highly structured epithelial tissues. In this study, we propose a novel model of cancer progression that considers a spatially structured cell population where clones expand via adaptive waves. This model is used to assess two different paradigms of asexual evolution that have been suggested to delineate the process of cancer progression. The standard scenario of periodic selection assumes that driver mutations are accumulated strictly sequentially over time. However, when the mutation supply is sufficiently high, clones may arise simultaneously on distinct genetic backgrounds, and clonal adaptation waves interfere with each other. We find that in the presence of clonal interference, spatial structure increases the waiting time for cancer, leads to a patchwork structure of non-uniformly sized clones and decreases the survival probability of virtually neutral (passenger) mutations, and that genetic distance begins to increase over a characteristic length scale Lc. These characteristic features of clonal interference may help us to predict the onset of cancers with pronounced spatial structure and to interpret spatially sampled genetic data obtained from biopsies. Our estimates suggest that clonal interference likely occurs in the progression of colon cancer and possibly other cancers where spatial structure matters.

  12. Reviewed in 'Cancer in Light of Experimental Evolution' by Sprouffske, Merlo, Gerrish, Maley, Sniegowski. Current Biology 22, (2012).
  13. Erik A. Martens and O. Hallatschek
    Interfering Waves of Adaptation Promote Spatial Mixing
    Genetics 189(3), 1045–1060 (2011)


    A fundamental problem of asexual adaptation is that beneficial substitutions are not efficiently accumulated in large populations: Beneficial mutations often go extinct because they compete with one another in going to fixation. It has been argued that such clonal interference may have led to the evolution of sex and recombination in well-mixed populations. Here, we study clonal interference, and mechanisms of its mitigation, in an evolutionary model of spatially structured populations with uniform selection pressure. Clonal interference is much more prevalent with spatial structure than without, due to the slow wave-like spread of beneficial mutations through space. We find that the adaptation speed of asexuals saturates when the linear habitat size exceeds a characteristic interference length, which becomes shorter with smaller migration and larger mutation rate. The limiting speed is proportional to μ1/2 and μ1/3 in linear and planar habitats, respectively, where the mutational supply μ is the product of mutation rate and local population density. This scaling and the existence of a speed limit should be amenable to experimental tests as they fall far below predicted adaptation speeds for well-mixed populations (that scale as the logarithm of population size). Finally, we show that not only recombination, but also long-range migration is a highly efficient mechanism of relaxing clonal competition in structured populations. Our conservative estimates of the interference length predict prevalent clonal interference in microbial colonies and biofilms, so clonal competition should be a strong driver of both genetic and spatial mixing in those contexts.

  14. Highlighted in ’Cutting through the complexity of cell collectives’ by Nadell, Bucci, Drescher, Levin, Bassler, Xavier. Proc. R. Soc. B, 280 (2013).

  15. Erik A. Martens
    Chimeras in a Network of Three Oscillator Populations with Varying Network Topology
    Chaos 20, 043122 (2010); arXiv:1003.2916

    hexagon We study a network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population. Using this system as a model system, we discuss for the first time the influence of network topology on the existence of so-called chimera states. In this context, the network with three populations represents an interesting case because the populations may either be connected as a triangle, or as a chain, thereby representing the simplest discrete network of either a ring or a line segment of oscillator populations. We introduce a special parameter that allows us to study the effect of breaking the triangular network structure, and to vary the network symmetry continuously such that it becomes more and more chain-like. By showing that chimera states only exist for a bounded set of parameter values, we demonstrate that their existence depends strongly on the underlying network structures, and conclude that chimeras exist on networks with a chain-like character.
  16. Erik A. Martens
    Bistable Chimeras on a Triangular Network of Oscillator Populations
    Phys. Rev. E, Vol. 82, 016216 (2010); arXiv:1003.2827

    hexagon We study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population. This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both chimeras are, as usual, born through a saddle-node bifurcation. As the coupling becomes increasingly local in nature they lose stability through a Hopf bifurcation, giving rise to breathing chimeras, which in turn get destroyed through a homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal of this scenario as we further increase the locality of the coupling, until it is annihilated through another saddle-node bifurcation.

  17. Erik A. Martens, C. R. Laing and S. H. Strogatz
    Solvable Model of a Spiral Wave Chimeras
    Phys. Rev. Lett., Vol. 104, 044101 (2010); arXiv:0910.5389

    Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here, we provide the first analytical description of such a spiral wave chimera and use perturbation theory to calculate its rotation speed and the size of its incoherent core.

    Featured in A. Motter, Spontaneous synchrony breaking, News and Views, Nature Physics 6 (2010)

  18. Erik A. Martens, E. Barreto, S. H. Strogatz, E. Ott, P. So and T. Antonsen
    Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
    Phys. Rev. E, Vol. 79, No.2 (2009); arXiv:0809.2129

    hexagon We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures about its behavior; ten years later, Crawford obtained the first analytical results by means of a local center manifold calculation. Nevertheless, many questions have remained open, especially about the possibility of global bifurcations. Here we derive the system’s stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians. Using an ansatz recently discovered by Ott and Antonsen, we show that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions. Depending on the parameters and initial conditions, the long-term dynamics evolves to one of three states: incoherence, where all the oscillators are desynchronized; partial synchrony, where a macroscopic group of phase-locked oscillators coexists with a sea of desynchronized ones; and a standing wave state, where two counter-rotating groups of phase-locked oscillators emerge. Analytical results are presented for the bifurcation boundaries between these states. Similar results are also obtained for the case in which the bimodal distribution is given by the sum of two Gaussians.

Ph.D. Thesis

  1. Erik A. Martens
    Cooperative Behavior in Networks of Coupled Oscillators
    Cornell University, USA (2009) eCommons@Cornell

Professional Activites

  1. Dynamics Days Europe, Szeged, Hungary, June 2017
    Organization of mini-symposium: "Complex patterns on networks"
  2. Rhythms in Complex Networks: From Theory to Experiment, 2014
    Dynamical Systems Interdisciplinary Network & Niels Bohr Institute, University of Copenhagen
    Main organizer of workshop.
  3. Dynamics Days Europe, Bayreuth, Germany, Sep 2014
    Organization of mini-symposium: "Chimera States in Biological Systems and Technological Applications"
  4. Trait-based approaches to Ocean Life (International Workshop), Copenhagen, Aug 2013.
    Co-organization of speed talks
  5. Dynamics Days Europe, Madrid, June 2013
    Organization of mini-symposium: "Emergent Dynamics in Coupled Oscillators"
  6. SIAM Conference on Applications of Dynamical Systems, Snowbird, May 2013
    Organization of mini-symposium: "Ensemble dynamics in experiments: from synchrony to chimera states"

Talks and Presentations

  1. SIAM Applications of Dynamical Systems. Snowbird, Utah, USA, May 2017.
  2. ICMS Winterschool Complexity. TU Eindhoven, Netherlands, February 2017.
    Invited Topical lecture.
  3. Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), Campus Universitat de les Illes Balears, Palma, Spain, January 2017.
    Invited Talk.
  4. Biomedical Engineering Group. Dept. of Electrical Engineering, Technical University of Denmark (DTU), Kgs. Lyngby, Denmark, January 2017.
    Invited Talk.
  5. International Conference on Control of Complex Systems and Networks. Collaborative Research Center 910 (SFB910), Heringsdorf, Germany, September 2016.
    Invited Talk.
  6. Dynamics Days Europe, Corfu, Greece, June 2016
  7. Workshop on synchronization and oscillators with generalized coupling, University of Exeter, United Kingdom, April 2016.
    Organizers: Chris Bick, Peter Ashwin, Kyle Wedgwood.
    Invited Talk.
  8. Dynamical Systems Interdisciplinary Network Seminar, Denmark, Oct 2016.
  9. Workshop on Cancer Evolution Through Space And Time (CEST), September 2015, Max-Planck Institute for Evolutionary Biology in Plön, Germany.
    Invited Talk: Cancer Progression and Evolution in Spatially Structured Tissues.
  10. Dynamics of Coupled Oscillators: 40 years of the Kuramoto Model, Dresden, July 2015
    Invited Talk: From Kuramoto to Mechanical Chimeras - and Back Again.
  11. SIAM Applications of Dynamical Systems, Snowbird, May 2015.
    Talk: Basins of Attraction for Chimera States.
  12. DPG Spring meeting, Berlin, Mar 2015.
    Invited Talk: Basins of attraction of chimera states.
  13. "Collective dynamics in coupled oscillator systems", Weierstrass Institute, Berlin, Nov 2014.
    Talk: Chimeras, Controlling and basins of attractions.
  14. Dynamical Systens Interdisciplinary Network Seminar, Denmark, Oct 2014.
    Talk: A tale of Greek monsters, the brain, control, and a bit about networks.
  15. Dynamics Days Europe, Bayreuth, Sep 2014.
    Talk: Controlling Chimeras.
  16. Istituto dei Sistemi Complessi - Consiglio Nazionale delle Ricerche CNR/INFN, Firenze, Italy, Dec 2013.
    Invited Talk: Chimera states - mythological monsters from math arise in the real world
  17. International Conference on Systems Biology, Copenhagen, Sep 2013.
    Talk: Spatial structure increases the waiting time for cancer
  18. Trait-based approaches to Ocean Life (International Workshop), Copenhagen, Aug 2013.
    Poster: Trait-based modeling of trophic chains and seasonal forcing
  19. Complex Motion in Fluids, DTU Summer School, Krogerup, Denmark, Aug 2013.
    Poster: Chimera States in Mechanical Oscillator Networks
  20. Dynamics Days Europe, Madrid, Jun 2013.
    Talk: Chimera states - how mythological monsters from math arise in the real world
  21. SIAM Applications of Dynamical Systems, Snowbird, USA, May 2013.
    Talk: Realization of Chimera States in a Network of Mechanical Oscillators
  22. Department of Engineering Sciences and Applied Mathematics, Northwestern University, Chicago, USA, May 2013.
    Invited talk: Chimera states - mythological monsters from mathematics in the real world
  23. Niels Bohr Institute, Copenhagen, March 2013
    Inivited Talk: Chimera States - or how mathematical creatures emerge in the real world
  24. Dept. of Biomedical Sciences, Copenhagen University, Dec 2012
    Inivited Talk: Chimera States - mythological monsters from mathematics in the real world
  25. Dynamics Days Europe, Gothenburg, September 2012
    Talk: (with Demian Battaglia): Self-organized routing of information in hierarchic networks of oscillators
  26. Dynamics Days Europe, Gothenburg, September 2012
    Talk: Realization of chimeras in a network of mechanical oscillators
  27. Department of Mathematics, Technical University of Denmark, April 2012
    Invited talk: Synchronization and symmetry breaking in coupled oscillators networks
  28. Centre for congestive diseases (N. Wright), Blizard Institute of Cell and Molecular Science, Queen Mary, University of London (UK), March 2012
    Invited talk: Evolution in Spatially Structured Cell Populations and Cancer Progression
  29. Institute for Chemistry and Biology of the Marine Environment (ICBM), Carl von Ossietzky University, Oldenburg (Germany), Februar 2012
    Invited talk: Adaptation in Spatially Extended Populations
  30. Statistical Physics / Theory of Chaos Group (Arkady Pikovsky), University of Potsdam, Germany, January 2012
    Invited talk: Speed of evolution in spatially structured populations and dynamics of interfering Fisher waves
  31. Niels Bohr Institute Copenhagen, Københavns Universitet, Copenhagen, January 2012
    Invited talk: Problems in oscillator dynamics and in evolutionary dynamics of spatially structured habitats
  32. XXXI Dynamics Days Europe, Oldenburg (Germany), September 2011
    Talk: Dynamical model of spatial evolution and cancer progression
  33. 75th Annual Meeting of the DPG and DPG Spring Meeting: Section on Statistical Physics and Biological Evolution, Dresden (Germany), March 2011
    Talk: Speed of evolution in spatially extended populations
  34. Laboratory of Genetics (de Visser Group), Wageningen University (NL), November 2010
    Invited talk: Speed of adaptation in spatially extended populations
  35. EMBO Conference Series: Experimental Approaches to Evolution and Ecology using Yeast, EMBL Heidelberg, September 2010
    Poster: Speed of evolution in spatially extended populations
  36. Annual Meeting of the Society for Molecular Biology and Evolution (SMBE) in Lyon, July 2010
    Talk: Speed of adaptation in spatially extended systems
  37. Statistical Physics / Theory of Chaos Group (Arkady Pikovsky), University of Potsdam, Germany, January 2010:
    Invited talk: Chimera states in 2D nonlocally coupled oscillator systems
  38. FOR 608 Nonlineary Dynamics, University of Bayreuth, Germany, October 2009:
    Talk: Coexistence of synchronized and desynchronized states in nonlocally coupled oscillator systems
  39. Dynamics Days Europe, Göttingen, August 2009:
    Talk: Coexistence of synchronized and desynchronized states in coupled oscillators
  40. SIAM Conference on Applications of Dynamical Systems, Snowbird, May 17 2009:
    Talk: Kuramoto model with bimodal distribution (minisymposium)
  41. Fluid Dynamics Group (Paul Steen), Chemical Engineering, Cornell University, Ithaca, November 2008
    Invited Talk: Pattern formation in fluids
  42. Gordon Conference, Nonlinear Science, Maine, 2005:
    Poster: Pattern formation in fluids: polygonal hydraulic jumps
  43. Complex Motions in Fluids, Summer School at Krogerup Højskole, Denmark
    Talk: The hydraulic jump and Its polygonal regime

2010 Erik (technique by Sven)