Robust persistence for semidynamical systems

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Global dynamics of a PDE in-host viral model (2014, background): “From the above claims, it follows that any forward orbit of t in M∂ converges to (u∗1, 0, 0) which is isolated in X+ and W s(u∗1, 0, 0) ∩ W0 = ∅, where W s(u∗1, 0, 0) is the stable set of (u∗1, 0, 0) (see [35]).”
Global dynamics of zooplankton and harmful algae in flowing habitats (2013, unknown): “Further, {E0} and {E1} are isolated in X and W ({Ei}) ∩ X0 = ∅, ∀ i = 0, 1, where W ({Ei}) is the stable set of {Ei}, i = 0, 1 (see [31]).”
Dynamics of a host-pathogen system on a bounded spatial domain (2015, background): “From the above claims, it follows that any forward orbit of Ψ(t) in M∂ converges to M1∪M2 which is isolated in X and W(Mi)∩W0 = ∅, ∀ i = 1, 2, where W(Mi) is the stable set of Mi, i = 1, 2 (see [30]).”
Global Attractors and Steady States for Uniformly Persistent Dynamical Systems (2005, methodology): “We note that the concept of general ρ-persistence was used in [27, 23, 30].”