EVENT DETAILS AND ABSTRACT

Title: Multiple scale analysis and local models generate low-dimensional maps
Speaker: Robert Clewley
Speaker Info: Boston University
Brief Description:
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Abstract:

Systems of oscillators described by ODEs arise commonly in the natural sciences, often with multiple time-scales. State-dependent coupling can add to the complexity, introducing new time-scales. These time-scales may not be explicit in the equations.We consider a computational technique that can be used to reduce the study of such networks, near a known attractor, to a set of low-dimensional approximate models. We find this conceptually related to a center manifold reduction. The technique adds rigor to intuitive reduction techniques that are ubiquitous in modeling high-dimensional coupled systems. In particular, it quantifies the robustness and parametric dependence of coherent temporal activity in more detail than a return-map stability analysis of periodic orbits, because it provides information along the entire length of the trajectory. As an example we describe the analysis of a network of Hodgkin-Huxley equations for biological membrane excitability.