Stabilization in a two-species chemotaxis system with a logistic source

By J. Castillo, Michael Winkler. 2012

209 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Oncology

View Paper: https://www.semanticscholar.org/paper/1476d9c3281300ad29804711118c37c92b95552b

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Citations in the corpus

Boundedness in a two‐species chemotaxis system (2015, background): “D 0), in the case of a1, a2 2 Œ0, 1/, the authors in [4] have proved that the system (1.”
Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening (2014, background): “Similar statements on global attractivity of spatially constant equilibria have been derived for chemotaxis systems involving two species interacting through chemotaxis and Lotka-Volterra-type competition under appropriate assumptions on the dominance of cell kinetics relative to chemotaxis ([30], [”
On a parabolic–elliptic system with gradient dependent chemotactic coefficient (2018, background): “In the last years, linear diffusion of the biological especies ”u” has been replaced in different ways: • by nonlinear diffusion at the form −div(φ(u)∇u), see for instance Wrzosek [39], Cieslak and Mortales-Rodrigo [16], Cieslak and Winkler [17], Winkler [38].”
Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant (2015, background): “In Tello and Winkler [20] the Parabolic–Parabolic–Elliptic problem is analyzed under “weak” competitive assumptions, which drive it to positive homogeneous steady states.”
Boundedness vs.blow-up in a two-species chemotaxis system with two chemicals (2015, background): “Such types of interplay, as found relevant in various biological applications ([15], [31], [21]), so far have been studied primarily in cases when two species produce the same signal the gradient of which directs their movement ([1], [9], [8], [37], [32]).”
On the weakly competitive case in a two-species chemotaxis model (2016, methodology): “4) Result and proof of [43] have successfully been extended to a setting of even more species in [47], the condition being analogous to (1.”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, methodology): “1) has been addressed in [35] for the case of weak competition when both a1 < 1 and a2 < 1, and in [32] for the case a1 > 1 and a2 < 1.”