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Exact(17)
Here (omega(x)) is the forward limit set of x.
From Theorem 4.1, S is the limit set of solutions to the CSDDEs (1.1).
Lemma 2. With probability 1, the sequence,, converges to some limit set of the ODE (16).
Therefore, the stronger conditions are needed to locate the limit set of the CSDDEs (1.1).
For this end define to be the limit set of, that is, the set of all cluster points of the sequence, and to be the limit set of for.
The omega limit set of a total trajectory (f(t)) is (mathcal {A}_{1}=mathcal{A}capGamma_{0}).
Similar(43)
We use to stand for the weak ω-limit set of.
The weak ω-limit set of {x n }, ω ω {x n }, is a subset of.
Hence the ω-limit set of the separatrix has to be the vertex of the parabola.
In addition, the ω-limit set of B is the attractor (mathcal {A}=omega(B)).
Let ω({x n }) be the ω-limit set of {x n }.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com