Abstract: 
The analysis of synchronization in networks of nonlinear systems is important in a variety of research fields in science and engineering as well as in mathematics. In the human nervous system, synchronization can be beneficial, allowing for production of a vast range of behaviors such as generation of circadian rhythms and emergence of organized bursting in pancreatic beta-cells; or detrimental, causing disorders such as Parkinson’s disease and epilepsy.

In realistic networks that feature heterogeneous nodes and nonuniform coupling structure, complex patterns of synchronization emerge. Finding the conditions that foster synchronization in networked systems is critical to understanding a wide range of biological and mechanical systems. In this talk I introduce several synchronization patterns and identify when synchronization occurs and explain its dependance on parameters such as network structure, coupling weights, and intrinsic nodal dynamics. 

As a real application of synchronization in biological settings, I show synchronous phenomena in central pattern generators (CPGs). CPGs are sophisticated circuits that can generate complex locomotor behaviors and even switch between different gaits. I discuss the mechanism of gait transition in an oscillator model of CPGs in insects.