I study pattern formation in biology using differential equations and dynamical systems theory. My work is inspired by oscillatory dynamics and spatial localization of proteins in yeast and neurons. I use dynamical systems theory, perturbation and bifurcation theory, and stochastic simulations to understand mathematical models.

Publications

F. Paquin-Lefebvre, B. Xu, K. DiPietro, A. Lindsay, A. Jilkine. Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations.  J. Theor. Biol. 497, 110242 (2020).

M. Panaggio, M. Ciocanel, L. Lazarus, C. Topaz, B. Xu. Model reconstruction from temporal data for coupled oscillator networks. Chaos 29, 103116 (2019).

B. Xu, H.W. Kang, A. Jilkine. Comparison of deterministic and stochastic regime in a model for Cdc42 oscillations in fission yeast. Bull. Math. Biol. 81(5) 1268-1302 (2019).

B. Xu, A. Jilkine. Modeling the dynamics of Cdc42 oscillation in fission yeast. Biophys. J. 114 711-722 (2018).

B. Xu, P. Bressloff. A theory of synchrony for active compartments with delays coupled through bulk diffusion. Physica D 341 45–59 (2017).

B. Xu, P. Bressloff. A PDE-DDE model for cell polarization in fission yeast . SIAM J. Appl. Math 76 1844–1870 (2016).

B. Xu, P. Bressloff. Model of growth cone membrane polarization via microtubule length regulation. Biophys. J. 109 2203-2214 (2015).

P. Bressloff, B. Xu. Stochastic active-transport model of cell polarization. SIAM J. Appl. Math 75 652-678 (2015).

W. Ding, X. Liang, B. Xu. Spreading speeds of N-season spatially periodic integro-difference models. Discrete Contin. Dyn. Syst 33 3443-3472 (2013).

PhD Dissertation: Mathematical models of cell polarization. University of Utah, 2017.