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Differential Dynamical Systems with Biological Applications


Projects:
Cell Cycle Dynamics in Yeast - with Dr. Todd Young, Dr. Bastien Fernandez, Dr. Erik Boczko, Gregory Moses, Gong Xue, and Nathan Breitsch


A 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 work includes:
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.
cluster number animation


Pulmonary Innate Immunity
- with 
Dr. Todd Young and Dr. Erik Boczko

A 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 patients.

Publications:

Iyer, R. Meixner, J. Buckalew, R. (2008) On on optical inertial navigation system--part I. IEEE Transaction on automatic control. V.53(8):1850-1863

Young, 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.

Young, T. Buckalew, R. May, A. Boczko, E. A low dimensional dynamical model of the initial pulmonary innate response to infection. Mathematical Biosciences (2012) 235(2):189-200.

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