Family of quadratic differential systems with invariant hyperbolas:a complete classification in the space R^12
In this article we consider the class QS of all non-degenerate quadratic systems. A quadratic polynomial differential system can be identified with a single point of R^{12} through its coefficients. In this paper using the algebraic invariant theory we provided necessary and sufficient conditio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/162/abstr.html |
| Summary: | In this article we consider the class QS of all
non-degenerate quadratic systems. A quadratic polynomial
differential system can be identified with a single point of
R^{12} through its coefficients. In this paper using
the algebraic invariant theory we provided necessary and
sufficient conditions for a system in QS to have at least
one invariant hyperbola in terms of its coefficients. We also
considered the number and multiplicity of such hyperbolas. We
give here the global bifurcation diagram of the class QS
of systems with invariant hyperbolas. The bifurcation diagram is
done in the 12-dimensional space of parameters and it is
expressed in terms of polynomial invariants. The results can
therefore be applied for any family of quadratic systems in this
class, given in any normal form. |
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| ISSN: | 1072-6691 |