Original article: Center conditions and cyclicity for a family of cubic systems: Computer algebra approach

Authors:
Brigita FerčEc;Adam Mahdi
Affiliations:
Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia;Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695, USA and Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30 ...
Venue:
Mathematics and Computers in Simulation
Year:
2013

Citing 4
Cited 0

Gröbner bases and primary decomposition of polynomial ideals

Journal of Symbolic Computation
Normalizable, Integrable, and Linearizable Saddle Points for Complex Quadratic Systems in \Bbb C2

Journal of Dynamical and Control Systems
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Tutorial: Symbolic computation and the cyclicity problem for singularities

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. To that end we overcome the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we also determine the number of limit cycles bifurcating from each component of the center variety.