\(QS8_{5}^{(0)}\)

Description

Topological configuration of singularities: \(s,s,a,a;N\)

Phase Portrait

Topological Invariants

TCSP	Fin Sep	Inf Sep
\(8\)	\(4431\)	\(31\)

The quadratic differential system

\[\begin{cases} \dot{x} = y \, (1-2 \, x) \\ \dot{y} = eps^{2} \, x/5-eps \, y+x^{2}+4 \, x \, y+3 \, y^{2} \end{cases}\]

has the following phase portrait done with P4. If you want, you may download the P4 file here.

With name \(Fig 5.102 S^2_{3,5}\) in {J. C. Artés, J. Llibre and A. C. Rezende}, Structurally unstable quadratic vector fields of codimension one, Birkhäuser/Springer, Cham, 2018, vi+267 pp.Note (for name \(Fig 5.102 S^2_{3,5}\)): The system has limit cycles with distribution \((0,1)\).
With name \(S^2_{3,5}\) in {J. C. Artés, R. E. Kooij and J. Llibre}, Structurally stable quadratic vector fields, Mem. Amer. Math. Soc. { bf 134} (1998), no.~639, viii+108 pp.; MR1432139

Through the border \(QS37_{7}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS23_{1}^{(0)}\).
Through the border \(QS37_{8}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS23_{1}^{(0)}\).
Through the border \(QS37_{9}^{(1)}\), by means of a bifurcation of type \(A\), we reach the neighbor \(QS23_{1}^{(0)}\).
Through the border \(QS8_{5}^{(1)}\), by means of a bifurcation of type \(D\), we reach the neighbor \(QS8_{1}^{(0)}\).
Through the border \(QS8_{4}^{(1)}\), by means of a bifurcation of type \(D\), we reach the neighbor \(QS8_{4}^{(0)}\).
Through the border \(QS73_{2}^{(1)}\), by means of a bifurcation of type \(C\), we reach the neighbor \(QS3_{1}^{(0)}\).
Through the border \(QS11_{8}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{7}^{(0)}\).
Through the border \(QS11_{9}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{7}^{(0)}\).
Through the border \(QS11_{12}^{(1)}\), by means of a bifurcation of type \(B\), we reach the neighbor \(QS10_{10}^{(0)}\).