In this talk, we discuss the influence of stochastic perturbations and
coupling on the synchronization behavior in networks of nonlinear
systems. First, we consider a homogeneous stochastic network where all
the systems are driven by a common noise and provide sufficient
conditions that guarantee complete synchronization. We show that
strong multiplicative noise can destroy synchronization, while
multiplicative noise with a linear lower bound can foster
synchronization. Then, we allow heterogeneity in the network and
assume that independent noises drive the systems. Heterogeneity leads
to approximate synchronization instead of complete synchronization. In
this case, similar to the homogeneous networks, we show that strong
multiplicative noise can be detrimental to synchronization. In
contrast, multiplicative noise with a linear lower bound can mitigate
desynchronization to some extent.

This is joint work with Vaibhav Srivastava.