Macroscopic description of spatially coupled oscillators with finite response times
Date and time:
Thursday, October 20, 2011 - 4:00pm
Synchronization in coupled oscillator systems is a paradigmatic example of collective emerging behavior from many simple interacting units. In various applications, the strength of the coupling between the oscillators is determined by their spatial proximity. In addition, in there is often a time delay or a finite response time to the signals between the oscillators. I will present and analyze a system consisting of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from other oscillators in its neighborhood. I will show how the microscopic dynamics of this system can be reduced to a macroscopic partial differential equation description, and show interesting spatiotemporal dynamical behaviors found using this description, including propagating fronts, persistent incoherent or synchronized spots, target patterns, and spiral waves. Finally, I will mention recent studies by others on the stability of some of these solutions.