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We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is…
Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
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 collective behavior of coupled dynamical units. Adaptive…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase…
We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…
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 seemingly unrelated types of dynamical networks has attracted…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
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 and solitary states. For an important subclass of the…
We investigate structural transitions in adaptive networks where node states remain fixed and only the connections evolve via state-dependent rewiring. Using a general framework characterized by probabilistic rules for disconnection and…
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural…
Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this…
We consider an ensemble of coupled oscillators whose individual states, in addition to the phase, are characterized by an internal variable with autonomous evolution. The time scale of this evolution is different for each oscillator, so…
The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have "dead zones", that is, the coupling…
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 can change their connectivity over time depending on…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…