Remark 3.2 Without delay and impulsive effect, Eq. (1) becomes stochastic neutral partial differential equations, which is investigated in [3].
Remark 3.3 In Eq. (1), provided △ x ( t k ) = 0, Eq. (1) becomes stochastic neutral partial differential equations without impulsive effects, that is to say, our Theorem 3.1 is effective for it.
The first proposes a model with two physiologically plausible lumped oscillators; on exposure to opiates, they propose that the coupling becomes stochastic in time (one has to read the supporting information to [4] to find this), but we can generate the observed behaviour with deterministic chaos, which we consider more satisfactory than invoking stochastic coupling.
In this regime, the observed reaction rate becomes stochastic in time, reflecting the fluctuation of the enzyme conformations.
Replicate samples diluted below 10 molecules per assay have scattered CT values because the presence of a genome per tube becomes stochastic (Figure 1b).
These functions were then stretched or skewed for other read lengths, and new transition probabilities were derived by evaluating the spline function at the appropriate positions and rescale the rows, so that the matrix becomes stochastic.
Besides, if a i j ( x ) ≡ 0, 1 ≤ i, j ≤ n, then the processes become deterministic stochastic processes.
PVCap is shown to delay the average hydrate nucleation time and also causes hydrate nucleation to become more stochastic.
If (b_{ij}(r)=c_{ij}(r)=0), (sigma_{i}(r)=beta_{ij}(r)=gamma_{ij}(r)=0), model (8) becomes a stochastic Lotka Volterra model with Markovian switching, where the sufficient conditions of the stochastic permanence and extinction were presented by Liu et al. [16].
Such kind of equations becomes a stochastic Hamilton system when taking random noise into consideration, which also can be called the forward backward stochastic differential equations (FBSDEs).
