Pattern Formation in Coupled Cell Networks
The general topic of Rubin's research is spatio-temporal pattern formation in coupled cell networks. The overall goal of this research is to understand how the intrinsic dynamics of network elements interact with the architecture and properties of coupling to drive network activity.
To this end, Rubin primarily uses and develops techniques in geometric singular perturbation theory, bifurcation theory, Evans function theory for stability analysis, as well as map-based reduction methods. Much of his work is motivated by biological applications, particularly those arising from networks of neurons. Some of Rubin's recent work, for example, has considered transitions in activity patterns in respiratory pacemaker networks, analysis of tremor and deep brain stimulation in Parkinson's disease, spike-timing dependent synaptic plasticity, and reduced models of the inflammatory response.