Self-induced switchings between multiple space-time patterns on complex networks of excitable units

We report on self-induced switchings between multiple distinct space--time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly resemble a random process, although the system is deterministic. We show that a chaotic saddle -- which contains all the patterns as well as channel-like structures that mediate the transitions between them -- is the backbone of such a pattern switching dynamics. Our analyses indicate that essential ingredients for the observed phenomena are that the system behaves like an inhomogeneous oscillatory medium that is capable of self-generating spatially localized excitations and that is dominated by short-range connections but also features long-range connections. With our findings, we present an alternative to the well-known ways to obtain self-induced pattern switching, namely noise-induced attractor hopping, heteroclinic orbits, and adaptation to an external signal. This alternative way can be expected to improve our understanding of pattern switchings in spatially extended natural dynamical systems like the brain and the heart

Complexity and irreducibility of dynamics on networks of networks

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh--Nagumo oscillators. For a large range of within- and between-network couplings, the network exhibits a variety of dynamical behaviors, previously described for single, uncoupled networks. We identify a region in parameter space in which the interplay of within- and between-network couplings allows for a richer dynamical behavior than can be observed for a single sub-network. Adjoining this atypical region, our network of networks exhibits transitions to multistability. We elucidate bifurcations governing the transitions between the various dynamics when crossing this region and discuss how varying the couplings affects the effective structure of our network of networks. Our findings indicate that reducing a network of networks to a single (but bigger) network might be not accurate enough to properly understand the complexity of its dynamics.Comment: 8 figure

BPSB/combine-p-values-discrete: Version 1.2.0

Added direction service function to find out in which direction a two-sided combined p value leans. Fixed Wilcoxon's signed-rank which broke due to a SciPy update. Some improvements to documentation

An impulse to the ground to end rolling with slipping

Several scenarios used to teach mechanics feature a rolling motion with slipping that transitions to one without slipping through friction with the ground. We present a compact approach for determining the final velocity in these scenarios: we summarise the transition by introducing an impulse that is transferred to the ground and account for it in the conservation of angular and linear momentum. In contrast to common approaches, we do not require any assumptions on the friction. Our approach thus serves to illustrate how using conservation laws and collisions allows to simplify problems by summarising complex interactions. We exemplify our approach with three scenarios: a sliding ball starting to roll, a turning wheel being released onto the ground, and a braking monowheel