Sentence examples for multiple positive equilibria from inspiring English sources

BioNetX is used to analyze uni-molecular and bi-molecular reaction networks for the existence of multiple positive equilibria in [ 19, 20].

A special case of this test is the Jacobian criterion, which provides a sufficient condition for excluding the existence of multiple positive equilibria and is based on the theory developed in [ 2, 13, 14].

If a given network admits multiple positive equilibria, in many cases the CRNT toolbox returns rate constant values such that the corresponding model system has at least two positive equilibria.

Cui et al., [ 18] showed that when the media impact is sufficiently strong, their model – with incidence rate being of the exponential form capturing the alertness to the disease of each susceptible individual in the population – exhibits multiple positive equilibria (also see [ 2]) which poses a challenge to the prediction and control of the outbreaks of infectious diseases.

Proposition 5 For any functional terms in Equations 17, satisfying the general assumptions formulated above, the system admits a unique equilibrium for large u > 0 or small u > 0. For some chioces of such functional terms, the system may have multiple positive equilibria x A, x B, x C,... ∈ IR3 (typically three) for intermediate values of u.

Besides the three boundary equilibria, (1.3) may have (componentwise) positive equilibria.

System (2.1) can have up to two positive equilibria.

Next we discuss the existence of positive equilibria.

We now analyze the local stability of the positive equilibria.

Correspondingly, system (1.2) can have one, two, or three positive equilibria.

All non-negative and positive equilibria are investigated, and the conditions that give rise to asymptotic behavior of these equilibria are examined.