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As a first step we discuss the infinite time extinction of the solution.
Similar to the first case, it is well known that g ( t ) vanishes in finite time since r < 1 and g ( t ) is a super-solution of (1.1) provided that u 0 ( x ) is small enough such that ∥ u 0 ∥ L ∞ ≤ g 0. Applying Proposition 2.1 to u ( x, t ) and g ( t ) guarantees the finite time extinction of u ( x, t ).
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We first look at the unstructured model; this yields a singular system of ordinary differential equations having interesting dynamical features, such as finite time extinction or persistence of populations.
For now, he is more in the mood to sit and reflect on grand subjects such as time, extinction and the attainment of what Teilhard de Chardin called the Omega Point: a zen-like state of relinquished consciousness.
For example, under the same conditions, Figure 4(b) shows that the mean time to extinction of the stochastic model is less than the time in the deterministic model.
Below we compute the mean time to extinction of a family of the given size for different versions of BDIM; the mean time to extinction of the largest family in the given genome is of particular interest.
Figure 4 a Time resolved extinction of the formation of the silver nanoprism via coalescence processes.
Second, what is the estimated time for extinction of a stable steady state in the presence of multiplicative extrinsic noise (Sections 5 and 6)?
We now use the path integral representation of the conditional probability (Equation 5.13) in order to estimate the time to extinction of a metastable nontrivial state.
Another important topic in population biology is estimating the time to extinction of a population in the presence of weak intrinsic or extrinsic noise sources, after having successfully invaded a given spatial domain [20].
After the demise of the concept of the MVP, PVA began to be performed largely to estimate other parameters, especially the expected time to extinction of a population the estimation of which does not require any conventional choices see the entry on conservation biology.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com