Martin Hasler

TL;DR: This paper elucidates the relation between network dynamics and graph theory and proposes a new general method to determine global stability of total synchronization in networks with different topologies that combines the Lyapunov function approach with graph theoretical reasoning.

TL;DR: In this article, the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons was studied and it was shown that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network.

TL;DR: It is proved that for the blinking model, a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length, which is more efficient than a structure of fixed random connections.

TL;DR: While the optimal receiver provides the base for assessing the potential of chaos-based schemes in this application, suboptimal versions thereof as presented in the paper allow efficient implementations.

TL;DR: Using the mathematical properties of self-kronecker-production of small size random matrices, a simple but effective method is presented to optimize the reservoir of an echo state network given a certain task.