October 24, 2013
The evolution in time of systems that are studied by biologists, chemists, physicists or engineers is often described by coupled nonlinear differential equations. Difficult to solve exactly, it is advantageous to study these equations and their solutions qualitatively. Will the system oscillate; and if so, will oscillations be periodic or chaotic? How do qualitatively different solutions arise as parameters are changed? In this talk, I will take such a point of view and discuss how this view informs our understanding of the fascinatingly complex behavior of some experimental systems, such as a chaotic water wheel and optoelectronic feedback oscillators. For example, I will discuss a particularly intriguing form of collective behavior that arises when several optoelectronic oscillators are coupled to form a network. Under certain conditions the entire network will oscillate chaotically and in synchrony, in spite of the signal propagation delays in the coupling links.