novel feedback mechanism for Yeast Autonomous Oscillation was proposed.
The feedback is modeled as a system of coupled ordinary differential
equations, or as a partial differential equation. In both cases, the
coupling is more complicated than in typical DE models. Some of our
General existence and stability results for a broad range
of clustered and non-clustered solutions of the basic ODE model
Extensions of these results to models including a gap or a
mediating agent to increase biological realism
Preliminary results on the infinitie-dimensional analog
using PDE conservation law techniques
The following animation shows the number of clusters forming in
the mediated model with negative linear feedback after approximately
500 cell cycles in the mediated model with alpha ranging between 0.1
and 5.0. The regions of stability begin forming near the center and
spread outward in a large series of bifurcations.
new model of the immune system of the lungs is proposed, wherein the
innate (nonspecific) system is the chief factor for infection dynamics
of pneumonia. Work in conjunction with Erik Boczko's team on a novel
form of pulmonary infectious agent monitoring in intensive care
Iyer, R. Meixner, J.
Buckalew, R. (2008) On on optical inertial navigation system--part I. IEEE Transaction on automatic
T. Fernandez, B. Buckalew, R. Moses, G. Boczko, E.
Clustering in cell cycle dynamics with general response/signaling
feedback. Journal of
theoretical biology 292:103-115.
T. Buckalew, R. May, A. Boczko, E. A low dimensional
dynamical model of the initial pulmonary innate response to infection. Mathematical Biosciences
Buckalew, R. Cell Cycle Clustering in a Nonlinear Mediated
Feedback Model. Preprint
Gong, X, Buckalew, R, Young, T, Boczko, E, Cell Cycle
Dynamics in a Response/Signaling Feedback System with a Gap. Preprint