For the given chemotaxis model, uniform persistence holds when m ≥ 1; the positive equilibrium is linearly stable for χ0 below a parameter-dependent threshold χ*(u*) and unstable above it, with exponential convergence under stated conditions.
Nachr.290(2017), no
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Quantitative estimates and weak convergence rates are derived for the Euler-Maruyama discretization of α-stable SDEs with bounded or Besov-negative drifts.
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Chemotaxis models with signal-dependent sensitivity and a logistic-type source, II: Persistence and stabilization
For the given chemotaxis model, uniform persistence holds when m ≥ 1; the positive equilibrium is linearly stable for χ0 below a parameter-dependent threshold χ*(u*) and unstable above it, with exponential convergence under stated conditions.
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Euler--Maruyama scheme for $\alpha$-stable SDE with distributional drift
Quantitative estimates and weak convergence rates are derived for the Euler-Maruyama discretization of α-stable SDEs with bounded or Besov-negative drifts.