Rings of delay-coupled oscillators: Dynamics, correlation and synchronization

Delay-coupled systems form a very active and competitive field in the
context of general oscillators, excitable systems, lasers, neurons
and many more. Also, as complex networks of delay-coupled oscillators
become ever more commonplace, there is an essential need to deeply
understand the dynamical properties of simple network motifs such as
rings and chains. In this seminar, we investigate the emergence of
the chaotic dynamics in a ring of delay-coupled nonlinear
oscillators. By doing so, we answer a long-standing question in the
field of delay-coupled oscillators: How does the chaotic dynamics
from an oscillator subject to delayed feedback compare to general and
more complex delayed coupling systems such as a ring of many
elements?. We find that knowing some properties of the delayed
feedback system we can predict the correlation and spectral
characteristics properties of the dynamical behavior of delay-coupled
systems precisely. We show that these results are not restricted to
lasers, but are a fundamental property of a wide class of delay
systems. From an application point of view, the broadband spectrum of
the dynamics generated by the system under study, the expectation
that the time delay can probably not be identified from the dynamics
and the fact that two elements can be synchronized via an
uncorrelated mediator, can have major implications in the field of
encrypted communications.