  We examine a system of N=2 coupled non-linear delay-differential equations
representing financial market dynamics. In such time delay systems, coupled
oscillations have been derived. We linearize the system for small time delays
and study its collective dynamics. Using analytical and numerical solutions, we
obtain the bifurcation diagrams and analyze the corresponding regions of
amplitude death, phase locking, limit cycles and market synchronization in
terms of the system frequency-like parameters and time delays. We further
numerically explore higher order systems with N>2, and demonstrate that limit
cycles can be maintained for coupled N-asset models with appropriate
parameterization.
