Learning of Complex Networks through Adaptive Synchronization of Chaos
Tuesday, October 9, 2012 - 3:15pm - 4:30pm
Department of Mechanical Engineering, University of New Mexico
In this talk I consider situations where time-evolving chaotic systems couple together to form a dynamical complex network. In the case in which the individual systems that are coupled are identical and appropriate coupling is employed, such networks may exhibit synchronization; that is, all the systems converge onto a common synchronized chaotic time-evolution. I present two applications of synchronization of chaos in networks. First, after presenting a review of the master stability function approach to network synchronization [Pecora
and Carroll, 1998], I show how appropriate decentralized adaptive strategies can be devised to synchronize and identify the temporally-evolving couplings of a complex sensor network (‘learning the network topology’ ). I present results from an experiment carried out in the Laboratory for Nonlinear Dynamics at the University of Maryland, where an adaptive sensor network based on this technique has been implemented and tested. Second, I present an extension of this approach to time-varying networks formed of interacting mobile robots or
mobile platforms. Each robot is assumed to be equipped with a chaotic oscillator and connected to the others by wireless. By using the strategy, each robot can adaptively estimate changes in the local network topology in a context of limited information. For example, if some of the robots are lost or separate from the rest of the group, this can be sensed. I discuss limitations as well as advantages of this technique, and its generalization to dierent problems such as that of estimating unknown communication-delays between coupled mobile
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