Two pervasive aspects of the brain motivate this project: brain rhythms and feedback connectivity. Rhythms indicating partial synchronization, neurons acting in unison, are ubiquitously observed in the brain by EEG and other techniques. But their function is still not well understood; certain rhythms tend to be enhanced when an animal pays attention to specific aspects of its environment. A second characteristic aspect of brain networks is their extensive feedback connectivity, which allows the processing of information in a brain area to be modulated by the very brain area that receives that information. This project will study rhythms in neuronal networks with feedback connectivity, investigating whether such targeted feedback allows selective synchronization of specific neurons and what functionalities emerge from it. It is expected that selective synchronization contributes to solving tasks similar to the cocktail-party problem of following the voice of a specific speaker among many people talking simultaneously. The research will focus on the olfactory system. There, a corresponding challenging task is, e.g., for a dog to track the faint smell of a drug or landmine amidst many other smells. The project will inform efforts to enhance the processing of the outputs of biologically motivated, event-driven technological sensors for complex stimulus scenes. The training of graduate and undergraduate students in applied mathematics, neuroscience, and interdisciplinary communication skills is an integral part of this project.
The research will develop a combined neuronal network model for the olfactory bulb and the piriform cortex. Incorporating aspects of the extensive structural plasticity of the olfactory system, the network will be adaptive, allowing the feedback connections to reflect previous experience. Biophysically detailed neuron models as well as highly simplified neuronal networks will be employed. Mathematically, the research will use and further various analytical and computational dynamical systems methods: weak coupling of mixed-mode oscillators and of delay-induced oscillators; weakly nonlinear analysis of neuronal populations interacting with multiple delays; bifurcation analysis of resonant, delay-induced Hopf bifurcations; numerical branch continuation. These approaches will be complemented by direct simulations.
