Sentence examples for limit circles from inspiring English sources
In Section 4, the bifurcations of limit circles are investigated, and five limit circles could be bifurcated from the origin.
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.
limit circle case, if and only if system ( S λ ) is in the limit point case, resp.
Since the solution should be within the limit circle, as described in Section 2.4, we use the center of that circle as a starting point.
We also give an exact connection between the limit point or limit circle classification of the original system (in dimension 2n) and the augmented system (in dimension 4n).
In turn, the limit point or limit circle classification of the augmented system ( S λ ) is determined by the numbers 3n and 4n (Definition 4.7 and Corollary 4.8).
