Georgia Institute of Technology College of Sciences

https://gatech.zoom.us/j/95197085752?pwd=WmtJUVdvM1l6aUJBbHNJWTVKcVdmdz09

We will begin with a brief overview of several parallel and hybrid computing approaches including CUDA, OpenAcc, OpenMP, and OpenMPI, followed by a demonstration of how we can leverage these technologies to study complex dynamics arising from diverse nonlinear systems. First, we discuss multistable rhythms in oscillatory 4-cell central pattern generators (CPGs) of inhibitory coupled  neurons. We show how network topology and intrinsic properties of the cells affect dynamics, and how even simple circuits can exhibit a variety of mono/multi-stable rhythms including pacemakers, half-center oscillators, multiple traveling-waves, fully synchronous states, as well as various chimeras. We then discuss symbolic methods and parametric sweeps to analyze isolated neuron dynamics such as bursting, tonic spiking and chaotic mixed-mode oscillations, the bifurcations that underlie transitions between activity types, as well as emergent network phenomena through synergistic interactions seen in realistic neural circuits and animal CPGs. We also demonstrate how such symbolic methods can help identify the universal principles governing both simple and complex dynamics, and chaotic structure in various Lorenz-like systems, their key self-similar organizing structures in 2D parameter space, as well as detailed computational reconstructions of 3D bifurcation surfaces.