Motivation
Our collaborative proposal is centered around developing new conceptual frameworks and methods for analyzing networks of Wilson–Cowan oscillators with distributed delays.
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Firstly, our investigation is driven directly by the vital importance of both network coupling and temporal aspects in neural functioning. It is eminently necessary to study them together to observe their interplay.
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Secondly, it is motivated by the absence of general analytical results or even frameworks for the simultaneous study of these two aspects.
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Thirdly, the work is timely in terms of human imaging data currently available for analysis, allowing the investigators to explore modeling the translation between neural meanfield dynamics captured by Wilson-Cowan equations and empirically-driven applications to clinical neuroscience and mental health.
Goals
AIM 1: Analytical Extension
In a preliminary joint study on low-dimensional delay networks, we found specific conditions on the network geometry which simplified formal dynamic analyses. These analyses can be more broadly extended to generic networks and delay distributions, and then illustrated for a wide class of networks with specific desired architectures and delay structures.
AIM 2: Numerical Simulations
Numerical methods will be carefully selected to complement the formal approaches and potentially inform further analyses. We will use methods that we have developed specifically to capture dynamic behavior in arbitrary and stochastic networks (e.g. swarm algorithms and “probabilistic” bifurcation diagrams).
AIM 3: Applications to Empirical Brain Networks
We will explore applications of our modeling approach to questions in clinical neuroscience, driven jointly by network and delay aspects.