Pattern Formation in Active Media
Many biological and chemical systems exhibit regular patterns. One of
the more common patterns observed is the spiral wave. Such waves arise
in many different situations including certain chemical reactions,
electrical activity in the myocardium, and in aggregation patterns of
certain amoeba. Many mathematical models have been proposed to model
such phenomena and my research involves the analysis of
such models. Much of this work is done in collaboration with
Bard Ermentrout at the University of Pittsburgh.
The areas of mathematics involved in this work are
ordinary and partial differential equations,
dynamical systems theory, bifurcation analysis, and computer simulation
and animation.
