Directed adaptation of synchronization levels in oscillator communities.

We present an adaptive control scheme that realizes desired dynamics of an oscillator network with a given number of communities by adjusting the coupling weights between oscillators accordingly. The scheme allows, for example, to simultaneously establish different pregiven synchronization levels in the particular communities as well as phase relationships between them. We apply the method in numerical simulations with all-to-all and randomly coupled networks.

Autonomous learning by simple dynamical systems with delayed feedback.

A general scheme for the construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the dynamics towards the target performance. As an example, a system of coupled phase oscillators, which can, by changing the weights of connections between its elements, evolve to a dynamical state with the prescribed (low or high) synchronization level, is considered and investigated.

Noise as control parameter in networks of excitable media: Role of the network topology.

We analyze coupled FitzHugh-Nagumo oscillators on various network topologies, in particular random diluted and scale-free topologies, under the influence of noise. Similarly to globally coupled excitable units, noise acts as control parameter: changing monotonically its strength, the collective dynamical behavior varies from stable equilibrium solutions to coherent firing of a large fraction, and for even stronger noise to incoherent firing leading to chaotic behavior of the excitable elements. For strong noise the system is less sensitive to the network topology.

On the role of frustration in excitable systems.

We study the role of frustration in excitable systems that allow for oscillations either by construction or in an induced way. We first generalize the notion of frustration to systems whose dynamical equations do not derive from a Hamiltonian. Their couplings can be directed or undirected; they should come in pairs of opposing effects like attractive and repulsive, or activating and repressive, ferromagnetic and antiferromagnetic.

The complex network of global cargo ship movements.

Transportation networks play a crucial role in human mobility, the exchange of goods and the spread of invasive species. With 90 per cent of world trade carried by sea, the global network of merchant ships provides one of the most important modes of transportation. Here, we use information about the itineraries of 16 363 cargo ships during the year 2007 to construct a network of links between ports.

Self-correcting networks: function, robustness, and motif distributions in biological signal processing.

Statistical properties of large ensembles of networks, all designed to have the same functions of signal processing, but robust against different kinds of perturbations, are analyzed. We find that robustness against noise and random local damage plays a dominant role in determining motif distributions of networks and may underlie their classification into network superfamilies.

Design and statistical properties of robust functional networks: a model study of biological signal transduction.

A simple flow network model of biological signal transduction is investigated. Networks with prescribed signal processing functions, robust against random node or link removals, are designed through an evolutionary optimization process. Statistical properties of large ensembles of such networks, including their characteristic motif distributions, are determined.