@phdthesis{PereiradaSilva2007,
  author    = {Pereira da Silva, Tiago},
  title     = {Synchronization in active networks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14347},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {In nature one commonly finds interacting complex oscillators which by the coupling scheme form small and large networks, e.g. neural networks. Surprisingly, the oscillators can synchronize, still preserving the complex behavior. Synchronization is a fundamental phenomenon in coupled nonlinear oscillators. Synchronization can be enhanced at different levels, that is, the constraints on which the synchronization appears. Those can be in the trajectory amplitude, requiring the amplitudes of both oscillators to be equal, giving place to complete synchronization. Conversely, the constraint could also be in a function of the trajectory, e.g. the phase, giving place to phase synchronization (PS). In this case, one requires the phase difference between both oscillators to be finite for all times, while the trajectory amplitude may be uncorrelated. The study of PS has shown its relevance to important technological problems, e.g. communication, collective behavior in neural networks, pattern formation, Parkinson disease, epilepsy, as well as behavioral activities. It has been reported that it mediates processes of information transmission and collective behavior in neural and active networks and communication processes in the Human brain. In this work, we have pursed a general way to analyze the onset of PS in small and large networks. Firstly, we have analyzed many phase coordinates for compact attractors. We have shown that for a broad class of attractors the PS phenomenon is invariant under the phase definition. Our method enables to state about the existence of phase synchronization in coupled chaotic oscillators without having to measure the phase. This is done by observing the oscillators at special times, and analyzing whether this set of points is localized. We have show that this approach is fruitful to analyze the onset of phase synchronization in chaotic attractors whose phases are not well defined, as well as, in networks of non-identical spiking/bursting neurons connected by chemical synapses. Moreover, we have also related the synchronization and the information transmission through the conditional observations. In particular, we have found that inside a network clusters may appear. These can be used to transmit more than one information, which provides a multi-processing of information. Furthermore, These clusters provide a multichannel communication, that is, one can integrate a large number of neurons into a single communication system, and information can arrive simultaneously at different places of the network.},
  language  = {en}
}