Sentence examples for has the unique equilibrium from inspiring English sources

Theorem 1 Assume that (2) has the unique equilibrium x ¯.

Similarly, it is easy to show that the function w ( z ) = α 2 − β 2 ( 1 − z ) e − z has no positive roots provided that α 2 ≥ β 2. Thus System (9) has the unique equilibrium point ( 0, 0,).

Performing the same calculations as for equation (15), we can show that for small ϵ > 0, equation (16) has the unique equilibrium q such that lim ϵ → 0 q = X ∗.

The system (3) has the unique equilibrium state Y* = 0m,1when for every j, a j ≠ 1, (see Proposition 3.1) and then the system is asymptotically stable in the large, when lim k → ∞ Y k = Y *.

with det ( s F - G ̃ ) = s + 1 2 s - 2 3. and since the matrix pencil doesn't have the finite eigenvalue 1 the system has the unique equilibrium state 0m,1and moreover since all the finite eigenvalues are inside the unite circle, the unique equilibrium state is asymptotically stable in the large and lim k → ∞ Y k = 0 m, 1.

Proof: Please see Appendix A. Theorem 2: The Nash equilibrium for the game model via convex pricing has the unique Nash equilibrium point [20].

Assume that Eq. (25) has the unique positive equilibrium (bar {x}).

If one of the above conditions holds, then system (1.4) has the unique positive equilibrium point, where (2.6).

(ii) If (R_{min}=R_{0}<1) and (B>0) then system (6) has the unique endemic equilibrium point  (E_{c}^).

If (R_{min}=R_{0}<1) and (B>0) then system (6) has the unique endemic equilibrium point  (E_{c}^).

So, system (6) has the unique endemic equilibrium point (E_{u}^) such that (I_{u}^>I_{min}).