### Stochastic Synchronization in Nonlinear Network Systems Driven by Intrinsic and Coupling Noise

Zahra Aminzare

Department of Mathematics

University of Iowa

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. **