## Bang-Bang Synchronization of Chaotic Systems |

** Mitrajit Dutta**

University of New Hampshire

October 31, 2005

4:30 pm

Bailey Hall 201

Patries and drinks will be served at 4:00 in Bailey Hall 204

There exists a large variety of nonlinear, physical systems whose evolution with time is completely deterministic; yet, owing to their defining hallmark of extreme sensitivity to initial conditions, they remain unpredictable for all practical purposes. In particular, if we follow the time evolution of an identical pair of such systems started at slightly different initial conditions, then the distance between the trajectories followed by the two systems are typically observed to diverge exponentially. Such systems are called chaotic. Over the last decade, there has been considerable interest in the synchronization of chaotic systems, particularly on account of its potential application to secure and covert communication. In this context, the setup often involves two identical systems described by the same set of nonlinear evolution equations that lead to the same chaotic attractor. A scalar signal stream is transmitted from one of the two systems (the transmitter) to the other (the receiver), in the hope that it can be used to synchronize the receiver to the transmitter. In this talk, a novel method of synchronization will be presented where the synchronizing signal is a series of spikes, rather than a continuous, scalar signal. In this scheme, the timing between the spikes is all that matters, and the details of the shape and the size of the spike (height, width etc.) are of no consequence. These properties should make the method interesting for applications in noisy environments. Computer simulation demonstrations illustrating the synchronization mechanism, as well as an application to communication, will be presented. Finally, the talk will be presented at a level accessible to students who have taken calculus and differential equations. Very little prior knowledge of chaos and chaotic systems will be assumed.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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