Sentence examples for equilibria without from inspiring English sources

According to Theorem 3.1, this difference will lead to the equilibria without predator, and the equilibria without predator is unstable.

For the equilibria without predator, it should satisfy the equation biggl(frac{x}{2K}-1 biggl) biggl( frac{tilde{r_{2}}x}{2A}+tilde{r_{1}}-tilde{r_{2}} biggr)=0.

How can we determine the processes that result in the stable species-lineages of punctuated equilibria without considering the properties of the enclosing regional or provincial ecosystems, which sometimes also appear to be stable over millions of years?

Standard nonlinear analysis is carried out and chaotic region is explored in the dynamical system without equilibria.

We identify repayment equilibria with and without exclusion and show that exclusionary equilibria are most likely when loans are large and there is significant within-group heterogeneity in the gains from the public good.

The possible action mechanisms of this combination of additives are analyzed and discussed on the basis of experimental data of hydrate phase equilibria (with and without additives), visual observations, and kinetics experiments.

Since in practice there is poor knowledge of the rate constants and binding affinities that occur in F (c), we are primarily interested in assessing a network's capacity for multiple equilibria or bistability without specifying these parameters, though all rate constants are assumed to be positive.

This paper deals with sampled feedback strategies applied on the class of switched affine systems without common equilibria.

E 1, E 2 are also positive equilibria for Equation (2.1) without diffusion, and when E 2 exists, it is unstable.

We first obtain the threshold dynamics on the global stability of the equilibria for the model without latent period, and then we analyze the stability and Hopf bifurcation for the model with the latent period.

Oxygen fugacities from the iron silicide involving equilibria (red symbols) were calculated without involving SiC and may hence be taken as independent confirmation of the f O2 -value of the SiC-forming reaction.