In a negative chemotaxis system with logistic growth and chemically induced death, solutions converge in L^∞ to extinction or a nontrivial homogeneous steady state according to the magnitude of constant chemorepellent supply relative to the growth rate.
Herrero-Hervás, M
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Global stability in a negative chemotaxis system with chemically induced lethality
In a negative chemotaxis system with logistic growth and chemically induced death, solutions converge in L^∞ to extinction or a nontrivial homogeneous steady state according to the magnitude of constant chemorepellent supply relative to the growth rate.