It is a fundamental challenge to understand how the function of a network is related to its
structural organization. Adaptive dynamical networks represent a broad class of systems that …

Adaptive networks change their connectivity with time, depending on their dynamical state.
While synchronization in structurally static networks has been studied extensively, this …

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and
technology. For example, adaptive couplings appear in various real-world systems, such as …

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural
sciences. In dynamical networks, phase transitions organize qualitative changes in the …

The human brain is a complex network whose ensemble time evolution is directed by the
cumulative interactions of its cellular components, such as neurons and glia cells. Coupled …

We propose an extension of the Fitzhugh-Nagumo model, which possesses a regime of
three coexisting stable states: resting equilibrium and two stable oscillatory states. Such a …

Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-
world systems of tremendous importance for our daily life. The investigation of these …

In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators.
We observe a variety of frequency-synchronized states such as phase-locked, multicluster …

Networks of coupled phase oscillators play an important role in the analysis of emergent
collective phenomena. In this article, we introduce generalized m-splay states constituting a …

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in
chemical, ecological, climate, or neural systems. Despite their importance, general …