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- ItemNonlinear dynamical properties of frequency swept fiber-based semiconductor lasers(Bristol : IOP Publishing, 2021) Slepneva, Svetlana; Pimenov, AlexanderWe investigate dynamics of semiconductor lasers with fiber-based unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behavior of such lasers using state-of-the-art experimental and analytical methods. Experimentally, we study the laser in static, quasi-static and synchronization regimes. We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterize these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilization of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterize the instability threshold both theoretically and experimentally, and demonstrate deterioration of the Fourier domain mode locking regime near the threshold.
- ItemOn complex dynamics in a Purkinje and a ventricular cardiac cell model(Amsterdam [u.a.] : Elsevier, 2020) Erhardt, André H.; Solem, SusanneCardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the occurrence of such phenomena and to decode their mechanisms. The focus of this paper is the investigation of dynamics of cardiac muscle cells described by systems of ordinary differential equations. This is generically performed by studying a Purkinje cell model and a modified ventricular cell model. We find chaotic dynamics with respect to the leak current in the Purkinje cell model, and EADs and chaos with respect to a reduced fast potassium current and an enhanced calcium current in the ventricular cell model — features that have been experimentally observed and are known to exist in some models, but are new to the models under present consideration. We also investigate the related monodomain models of both systems to study synchronisation and the behaviour of the cells on macro-scale in connection with the discovered features. The models show qualitatively the same behaviour to what has been experimentally observed. However, for certain parameter settings the dynamics occur within a non-physiological range.
- ItemA unified and automated approach to attractor reconstruction(London : IOP, 2021) Kraemer, K. H.; Datseris, G.; Kurths, J.; Kiss, I. Z.; Ocampo-Espindola, J. L.; Marwan, N.We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
- ItemBasin stability and limit cycles in a conceptual model for climate tipping cascades([London] : IOP, 2020) Wunderling, Nico; Gelbrecht, Maximilian; Winkelmann, Ricarda; Kurths, Jürgen; Donges, Jonathan F.Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland Ice Sheets (GIS) and West Antarctic Ice Sheets, the Atlantic meridional overturning circulation (AMOC), the El–Niño Southern Oscillation and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. By combining these two methodologies with a large-scale Monte Carlo approach, we are able to propagate the many uncertainties associated with the critical temperature thresholds and the interaction strengths of the tipping elements. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 °C above pre-industrial climate conditions, representing a highly undesired state where a majority of the tipping elements reside in the transitioned regime. For lower levels of warming, states including disintegrated ice sheets on west Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the GIS and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.
- ItemTowards dynamical network biomarkers in neuromodulation of episodic migraine(Berlin : De Gruyter, 2013) Dahlem, M.A.; Rode, S.; May, A.; Fujiwara, N.; Hirata, Y.; Aihara, K.; Kurths, J.Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.
- ItemSupermodeling by combining imperfect models(Amsterdam : Elsevier B.V., 2011) Selten, F.M.; Duane, G.S.; Wiegerinck, W.; Keenlyside, N.; Kurths, J.; Kocarev, L.SUMO (Supermodeling by combining imperfect models) is a three-year project funded under FET Open program with a starting date October, 1, 2010. We review some basic facts and findings of the SUMO project.
- ItemCardiac contraction induces discordant alternans and localized block(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Radszuweit, Markus; Alvarez-Lacalle, Enrique; Bär, Markus; Echebarria, BlasIn this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e. alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be pro-arrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e. from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.
- ItemAnalysis and simulation of a modified cardiac cell model gives accurate predictions of the dynamics of the original one(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Erhardt, André H.; Solem, SusanneThe 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good approximation of the original one. As a consequence, one can extract fairly precise predictions of the behaviour of the original model from the bifurcation analysis of the modified model. Thus, the findings of bifurcations linked to complex dynamics in the modified model - like early afterdepolarisations (EADs), which can be precursors to cardiac death - predicts the occurrence of the same dynamics in the original model. It is shown that bifurcations linked to EADs in the modified model accurately predicts EADs in the original model at the single cell level. Finally, these bifurcations are linked to wave break-up leading to cardiac death at the tissue level.