Phase entrainment in coupled time-delay systems
The notion of phase and phase synchronization in time-delay systems
are not well understood despite of our substantial understanding of
these phenomena in non-delay (low-dimensional) systems. We will discuss
briefly the drawbacks in estimating phase in time-delay systems
usually exhibiting highly non-phase-coherent hyperchaotic attractors
with complex topological properties. We will provide a brief note on the
different approaches that we have used in estimating phase and subsequently
identifying chaotic phase synchronization in coupled time-delay systems.
Further, we will demonstrate the existence of chaotic phase synchronization in
paradigmatic models such as a piecewise linear time-delay systems and
Mackey-Glass systems numerically and experimentally in
time-delay electronic circuits with a threshold nonlinearity.