Colloquium

The classic example of synchronised chaos arises when two identical oscillators are coupled together. If each has at least three degrees of freedom (dimensions of phase space) then it is possible for both to obey identical chaotic dynamics -- synchrony. This phenomenon has been studied because of potential applications to cryptography, but it also has applications elsewhere. The crucial issue here is the stability of the synchronous state, and how it can be lost as a parameter is varied. The bifurcation scenario turns out to be complicated, including the possibility of 'bubbling', where synchrony is repeatedly lost and regained. This effect is related to a lack of uniqueness of invariant measures on the synchronous state. More generally, we can consider a more complicated network, and ask the same questions. How does synchronised chaos arise? What sort of bifurcations do we expect? Again, we expect to find bubbling behavior, with similar criteria regarding stability. The talk will explore these questions, with a brief introduction to network dynamics and synchrony, and report on some numerical experiments related to the Rossler attractor.