Sentence examples for stochastic permanence from inspiring English sources

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By means of the M-matrix analysis and Lyapunov functions, we study stochastically ultimate boundedness and stochastic permanence, and the sufficient condition of stochastic permanence is given in Section 3.

In this section, we consider stochastic permanence and first study stochastically ultimate boundedness.

It then follows from Theorem 4.1 that system (7.1) is stochastically permanent, see Figure 3. Figure 3 Computer simulations of the stochastic permanence for system ( 7.1 ).

(Stochastic permanence).

Next we investigate stochastic permanence.

(Stochastic permanence and asymptotic properties).

end{aligned} Figure 4 Stochastic permanence.

See Figure 3. Figure 3 Stochastic permanence.

Next we investigate the stochastic permanence.

The proof of stochastic permanence is rather long and technical.

Sufficient conditions for the extinction, stochastic permanence, and global attractivity of system are obtained, respectively.

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