School of Mathematical and Statistical Sciences Faculty Publications and Presentations


Asymptotic Spreading for a Diffusive Chemostat System in Space-Time Periodic Environment

Document Type


Publication Date



This paper presents the dynamics that one microorganism spatially expands with two nutrients in space-time periodic environment. The generalized principal eigenvalue defined by the linear periodic parabolic operator is applied as a threshold to discuss the associated initial value problem. When the generalized principal eigenvalue is nonnegative, the solutions approach to the microorganism-extinction equilibrium uniformly. When the generalized principal eigenvalue is negative, the spreading speeds of the model are established when the initial distribution of microorganism has nonempty compact support, which are determined by a family of periodic parabolic eigenvalue problems. In the homogeneous environment, we show that the solutions locally uniformly converge to the microorganism-existent steady state by constructing upper and lower solutions. Finally, numerical simulations are performed to illustrate that the leftward or rightward spreading speed is approximately a constant under various circumstances.


Copyright © 2022, The Author(s), under exclusive licence to Springer Science Business Media, LLC, part of Springer Nature.

Publication Title

Journal of Dynamics and Differential Equations