Sentence examples for by a small parameter from inspiring English sources
We consider a family of stochastic differential equations with a drift depending on the past history and a delayed diffusion term perturbed by a small parameter ε>0.
We propose an analytical approximation to the wave-speeds of IDE solutions with periodic landscapes of alternating good and bad patches, where the dispersal scale is greater than the extent of each good patch and where the ratio of the demographic rates in the good and bad patches is given by a small parameter, denoted as ε.
The size, shape and distribution of the perforation are described by a small parameter.
As in [35], the bifurcating periodic solutions (y t, mu)) of system (3.1) are indexed by a small parameter ε.
Singularly perturbed differential equations are typically characterized by a small parameter ε multiplying some or all of the highest-order terms in the differential equations.
Due to the regularity of element arrangements, their geometries are specified by a small parameter set, such as aperture and number of elements or their spacings, which are directly related to aspects of performance [2, 6].
By defining a small parameter ε, associated with the size and the stiffness of the intermediate layer, we derive various limit models and their corresponding limit problems, by varying the thickness and rigidity ratios of the adherents and the adhesive layers.
Its evaluation is made numerically, according to the definition of the Cauchy Principal Value of an integral, by using a small parameter ε to isolate the singularity.
Kuo et al. [10] obtained an asymptotic solution depending on a small parameter by applying the perturbation technique to elastic beams on nonlinear foundations.
Sustainable yield on the evolutionary time-scale is highest when fishing is done by trawling, but only for a small parameter region.
One hierarchical approach to reduce the complexity, explored by Yin and Zhang [14], introduces a small parameter ε > 0 and leads to a singularly perturbed Markov chain α ε.
