Sentence examples for condition for persistence from inspiring English sources
These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence.
These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.
However, such mutual invasibility is a condition for persistence.
Unfortunately, conditions for persistence are poorly characterized, as are the larval dispersal patterns on which persistence depends.
Then, several conditions for persistence in mean and extinction of the disease are also established.
Moreover, the sufficient conditions for persistence in mean, extinction are obtained.
Theorem 2.1 describes sufficient conditions for persistence in the mean and extinction, which are derived from the stochastic analysis theory.
end{cases} (3) In model (3), the authors discussed in detail the conditions for persistence in mean and extinction of each epidemic disease.
Further, the conditions for persistence and extinction of the disease are also established, where a threshold is given in the case that the noise is small.
By using the stochastic analysis theory and differential inequality technology, we firstly obtain sufficient conditions for persistence in the mean and extinction.
Moreover, the sufficient conditions for persistence in mean, extinction are obtained in Section 4. For convenience and simplicity in the following discussion, for any sequence c(i), i ∈ S, we define.
