Spatiotemporal Regularity in Networks with Stochastically Varying Links

In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the network changes occur locally and independently at each node. Secondly we consider the case where the entire connectivity matrix changes with probability pt, i.e. the change is global. We show that network changes, occurring both locally and globally, yield an enhanced range of synchronization. When the connections are changed slowly (i.e. pt is low) the nodes display nearly synchronized intervals interrupted by intermittent unsynchronized chaotic bursts. However when the connections are switched quickly (i.e. pt is large), the intermittent behavior quickly settles down to a steady synchronized state. Furthermore we find that the mean time taken to reach synchronization from generic random initial states is significantly reduced when the underlying links change more rapidly. We also analyze the probabilistic dynamics of the system with changing connectivity and the stable synchronized range thus obtained is in broad agreement with those observed numerically.Comment: 15 pages, 8 figures, Keywords: Complex Networks, Temporal Networks, Synchronization, Coupled Map Lattic

Memristor: A New Concept in Synchronization of Coupled Neuromorphic Circuits

The existence of the memristor, as a fourth fundamental circuit element, by researchers at Hewlett Packard (HP) labs in 2008, has attracted much interest since then. This occurs because the memristor opens up new functionalities in electronics and it has led to the interpretation of phenomena not only in electronic devices but also in biological systems. Furthermore, many research teams work on projects, which use memristors in neuromorphic devices to simulate learning, adaptive and spontaneous behavior while other teams on systems, which attempt to simulate the behavior of biological synapses. In this paper, the latest achievements and applications of this newly development circuit element are presented. Also, the basic features of neuromorphic circuits, in which the memristor can be used as an electrical synapse, are studied. In this direction, a flux-controlled memristor model is adopted for using as a coupling element between coupled electronic circuits, which simulate the behavior of neuron-cells. For this reason, the circuits which are chosen realize the systems of differential equations that simulate the well-known Hindmarsh-Rose and FitzHugh-Nagumo neuron models. Finally, the simulation results of the use of a memristor as an electric synapse present the effectiveness of the proposed method and many interesting dynamic phenomena concerning the behavior of coupled neuron-cells