Events

We observe rare and recurrent large spiking events in a heterogeneous network of superconducting Josephson junctions (JJ) connected through a resistive load and driven by a radio-frequency (rf) current in addition to a constant bias. The intermittent large spiking events show characteristic features of extreme events (EE) since they are larger than a statistically defined significant height. Under the influence of repulsive interactions and an impact of heterogeneity of damping parameters, the network splits into three sub-groups of junctions, one in incoherent rotational, another incoherent librational motion and a third sub-group originating EE. We are able to scan the whole population of junctions with their distinctive individual dynamical features either in EE mode or non-EE mode in parameter space. EE migrates spatially from one to another sub-group of junctions depending upon the repulsive strength and the damping parameter. For weak repulsive coupling, all the junctions originate frequent large spiking events, in rotational motion when the average inter-spike-interval (ISI) is small, but it increases exponentially with repulsive interaction; it largely deviates from its exponential growth at a breakpoint where EE triggers in a sub-group of junctions. The probability density of inter-event-intervals (IEI) in the subgroup exhibits a Poisson distribution. EE originates via bubbling instability of in-phase synchronization.

To be announced

Modeling complex systems as networks have recently received much attention, as real-world systems usually consist of many coupled units. The dynamics of such coupled systems generically differ from the individual dynamics of single units and collective effects are in the focus of interest. Although heteroclinic cycles emerge robustly in various scenarios (e.g. in population dynamics, fluid dynamics, or game theory), systems of coupled heteroclinic cycles have not been extensively studied up to now.

He will first give a broad introduction to heteroclinic cycles and their dynamics, and subsequently present results on small coupled systems. In spite of their simple structure, they exhibit rich dynamics. In particular interesting is the emergence of different kinds of dimensional reduction, especially toward a synchronized state, and the multistability between them. Furthermore, parameter regions of transient chaos emerge which seems to exhibit non-standard scaling behavior.

To be announced

An adaptive coupling function based strategy is developed to induce first-order transition [ex- plosive/hysteresis synchronization (ES)] and investigate that phenomenon in networks of phase- frustrated oscillators. Firstly we consider Sakaguchi-Kuramoto dynamics on top of a multiplex networks and we establish that ES can emerge in all layers of a multiplex network even when one of the layers may not exhibit ES in the absence of the interlayer connections. We clearly identify the regions of the parameter space in which the multiplexity wins over the frustration parameter and network structure for the emergence of ES. Based on the mean-field analysis around the coherent state and a perturbative approach around the incoherent state we analytically derive the synchro- nization transition points (backward and forward) of all layers of the multiplex network as well as its monolayer counterpart satisfying a close agreement with the numerical results. In the next case the adaptive function is controlled by the time dependent synchronization order parameter in which order parameter can be used as multiplicative or more higher power terms which can enhance the hysteresis loop in the network. Based on mean field analysis, a semi-analytical formalism is developed, which can accurately predict the backward transition of synchronization order parameter. The strategy is robust and we have shown it can diminish (by inducing enhanced hysteresis loop) the contrarian impact of phase frustration in the network irrespective of network structure or frequency distributions.

Estimating resilience, i.e., the capability of a system to withstand perturbations while retaining its function, structure, and feedbacks, from time series of observations is an unsolved problem. Current methods either require in-depth knowledge of the system's underlying equations of motion (including the ability to arbitrarily perturb the system) or are based on assumptions that may not be fulfilled. Concerning the latter, accumulated knowledge indicates that associated data-driven methods are insufficient. In this talk, I will present a novel data-driven method to estimate resilience of spatially extended dynamical systems [1] based on a network approach proposed by Gao et al. [2]. Assuming that relevant aspects of the system's dynamics are captured by the temporally evolving coupling structure, which can be estimated employing well-known bivariate time series analysis techniques, we define states by recurring similar coupling structures. An estimate for resilience is than derived from the distance between these functionally defined states in a time-resolved manner. I will present an application of this approach by investigating the dynamics of the human epileptic brain, that recurrently transit into and out of the extreme event epileptic seizure as well as into and out of different physiological stages. Furthermore, I will discuss possible methodological and conceptual improvements and extensions.