Hughes, J. M., Modai, S., Edelstein-Keshet, L., Yochelis, A. Bistability of travelling waves and wave-pinning states in a mass-conserved reaction-diffusion system: From bifurcations to implications for actin waves, accepted for publication in the SIAM Journal on Applied Dynamical Systems.
Hughes, J. M., Martinez-Torres, C., Beta, C., Edelstein-Keshet, L., Yochelis, A. A dissipative mass-conserved reaction-diffusion system reveals switching between coexisting polar and oscillatory cell motility states, Chaos, 2025, 051103.
Alogrta, J., Fele-Paranj, A., Hughes, J. M., Edelstein-Keshet, L. Modeling and simulating single and collective cell motility, Cold Spring Harbor Perspectives in Biology, 2025, a041796.
Mitra K., Hughes, J. M., Sonner, S., Eberl, H.J., Dockery, J.D. Travelling waves in a PDE-ODE coupled system with nonlinear diffusion, Journal of Dynamics and Differential Equations, 2023, 36, 3037–3071.
Hughes, J. M., Eberl, H. J., Sonner, S. A mathematical model of discrete attachment to a cellulolytic biofilm using random DEs. Mathematical Biosciences and Engineering, 2022, 19, 6582–6619.
Gaebler, H. J., Hughes, J. M., Eberl, H. J. Contaminant removal in ceramic water filters by bacterial biofilms. In Recent Developments in Mathematical, Statistical and Computational Sciences; Wang, X.; Melnik, R.; Makarov, R.; Kunze, H.; Kilgour, D. M., Eds.; Springer International Publishing, 2021; Vol. 343, pp. 545–554.
Gaebler, H. J., Hughes, J. M., Eberl, H. J. Thermodynamic inhibition in a biofilm reactor with suspended bacteria. Bulletin of Mathematical Biology, 2021, 83, 10.
Hughes, J. M. A mathematical model of biofilm growth on degradable substratum. SIAM Undergraduate Research Online, 2020, 13, 94-115.