These peaks converge to the maximum of V as (hbarrightarrow0).
Particularly, in the interesting paper [5], the authors proved that the solutions of (1.2) have several peaks near the point of a maximum of V.
The black curve represents the critical manifold S of the fast subsystem (solid for stable fixed points, dashed for unstable), and the blue curve shows the maximum of v along the family of periodics P.
With the constant (kappa ) fixed, from (3.17) and (D_beta v(x_0)le 0), we obtain begin{aligned} M^2_1 le frac{2C}{kappa }. end{aligned} (3.18)We next consider the case that the maximum of v occurs at a point (x_0in Omega ).
The denominator is positive by the second order condition for a maximum of V, differentiating (5) yields ∂ V/∂ β=-0.5+l 1-l), and the expression in (6) has the same sign as d dτ l 1 - l = 1 - 2 l l ′ , which is negative for l>0.5 and l′<0.
If the elements of the set are uniformly distributed then the maximum of V function is directly affected by α value.
Simulating exclusive utilization of oleate resulted with an increased oxygen uptake to a maximum of v O 2 = 4.1101 mmol·min−1· l cell)−1, while only a minimal total substrate uptake rate was required (v s = 0.162 mmol·min−1· l cell)−1).
