I’ve just posted a paper to arXiv.org entitled “Competition between transients in the rate of approach to a fixed point“, by Judy Day, Jonathan Rubin and Carson C. Chow. The paper examines how long it takes to approach a fixed point. The problem was motivated by a biological phenomenon known as tolerance, where the body’s inflammatory response to a noxious stimulus is attenuated by a pre-exposure to that substance. We translated this problem into the question of given two orbits, under what conditions would one orbit “pass” another. We show that using general properties of the continuity of orbits and the concept of inhibition, a set of conditions for when tolerance can and cannot exist can be established. Transient dynamics have not been well studied and this paper represents an approach into the issue.
I recently wrote a scholarpedia entry on multiple scale analysis. It is a useful tool of applied mathematics.
Our paper “The Dynamics of Human Body Weight Change” just appeared in PLoS Computational Biology.