Sentence examples for singular equilibrium from inspiring English sources

A singular equilibrium function that maximizes the critical velocity level was identified, which was afterwards tested in particular cases of confined flows of interest, validating the resulting procedure.

Optimal singular equilibrium points have been obtained numerically for various discount rate in various cases.

Optimal singular equilibrium points are obtained numerically for various discount rates.

Therefore, at least one optimum singular equilibrium point in each from which ((x_{(1)}^, y_{(1)}^, E_{(1)}^)) is feasible from an ecological point of view.

From the above tables we conclude that there is at least one optimum singular equilibrium point in each from which ((x_{(1)}^,y_{(1)}^,E_{(1)}^)) is feasible from an ecological point of view.

This shadow price (tau_{i}(t)=lambda_{i}(t)e^{-mu t}), (i=1,2), should remain constant over time in singular equilibrium to satisfy the transversality conditions at ∞ (i.e. (lim_{trightarrow infty }lambda_{i}(t)=0) for (i=1,2)).

Qualitative analysis shows that there is a degenerate singular infection equilibrium.

As previously mentioned, both environmental policy and public perception in the USA reflect widespread belief in a singular 'natural' equilibrium state, enshrined in Clementsian ecological theory as the climax to which ecosystems will return if disturbances are removed.

For a singular optimal equilibrium solution, we use the steady state equations (12) and (13) in terms of (x^) and (y^=frac{x^{n}), hence (x^), (y^) and E can be taken as constant [35].

The bifurcation analysis indicates that (1.6) undergoes a Bogdanov-Takens bifurcation at the degenerate singular infection equilibrium which includes a saddle-node bifurcation, a Hopf bifurcation, and a homoclinic bifurcation.

Minimization of potential energy with Tikhonov regularization is adopted to solve the singular system of equilibrium equations resulting from the filtered designs.