All beauty, richness and harmony in the emergent dynamics of a complex system largely
depend on the specific way in which its elementary components interact. The last twenty-five …

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 …

Over the past two decades, complex network theory provided the ideal framework for
investigating the intimate relationships between the topological properties characterizing the …

Various systems in physics, biology, social sciences and engineering have been
successfully modeled as networks of coupled dynamical systems, where the links describe …

The emergence of large-scale connectivity and synchronization are crucial to the structure,
function and failure of many complex socio-technical networks. Thus, there is great interest …

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 …

We propose a concept to generate and stabilize diverse partial synchronization patterns
(phase clusters) in adaptive networks which are widespread in neuroscience and social …

Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It
is a slow-fast phenomenon characterized by a recurrent sequence of fast transitions …

Topological signals defined on nodes, links and higher dimensional simplices define the
dynamical state of a network or of a simplicial complex. As such, topological signals are …