Sentence examples for limit circle from inspiring English sources
The linear gains that control the two critical bifurcation conditions are derived according to the suitable criteria without using eigenvalues, and the nonlinear gains that control the stability of the created limit circle are analytically derived by utilizing the center manifold theory and normal form reduction.
If it is not limit circle, we say it is limit point.
limit circle case, when the rank of R + is n, resp.
Now, we will discuss the bifurcations of limit circle at the origin of the system.
It is a theorem that whether one is limit point or limit circle is independent of z.
In one dimension, this is related to a result of Kurss [401] who proved the result for continuous V although his argument doesn't need continuity (essentially it follows from a simple comparison argument for positive solutions and limit point-limit circle methods).
This analysis is based on our construction of limit-point (LP) and limit-circle (LC) solutions obtained recently in an earlier paper.
Suppose that L is a limit-circle case at t = + ∞.
These represent limit-circle and limit-point cases, respectively.
Theorem 3.1 L 2 is a limit-circle case at t = + ∞ if and only if L is a limit-circle case at t = + ∞.
