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.<\/p>\n
F. Paquin-Lefebvre, B. Xu, K. DiPietro, A. Lindsay, A. Jilkine.\u00a0<\/span>Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations<\/a>. \u00a0J. Theor. Biol. 497, 110242 (2020).<\/span><\/p>\n M. Panaggio,\u00a0M. Ciocanel,\u00a0L. Lazarus,\u00a0C. Topaz, B. Xu. Model reconstruction from temporal data for coupled oscillator networks<\/a>. Chaos 29, 103116 (2019).<\/p>\n B. Xu, H.W. Kang, A. Jilkine. <\/span>Comparison of deterministic and stochastic regime in a model for Cdc42 oscillations in fission yeast.<\/a>\u00a0<\/span>Bull.<\/span>\u00a0Math.<\/span>\u00a0Biol. 81(5) 1268-1302 (2019)<\/span>.<\/span><\/p>\n B. Xu, A. Jilkine. Modeling the dynamics of Cdc42 oscillation in fission yeast<\/a><\/strong>.\u00a0Biophys. J. 114 711-722\u00a0<\/i>(2018).<\/strong><\/p>\n B. Xu, P. Bressloff. A theory of synchrony for active compartments with delays coupled through bulk diffusion<\/a>.<\/strong> Physica D<\/i> 341 45\u201359 (2017).<\/p>\n B. Xu, P. Bressloff. A PDE-DDE model for cell polarization in fission yeast <\/a><\/strong>. SIAM J. Appl. Math<\/i> 76 1844\u20131870 (2016).<\/p>\n B. Xu, P. Bressloff. Model of growth cone membrane polarization via microtubule length regulation<\/a><\/strong>. Biophys. J.<\/i> 109 2203-2214 (2015).<\/p>\n P. Bressloff, B. Xu. Stochastic active-transport model of cell polarization<\/a><\/strong>.\u00a0SIAM J. Appl. Math<\/i> 75 652-678 (2015).<\/p>\n W. Ding, X. Liang, B. Xu. Spreading speeds of N-season spatially periodic integro-difference models<\/a><\/strong>. Discrete Contin. Dyn. Syst<\/i> 33 3443-3472 (2013).<\/p>\n