Results 11 to 20 of about 59,907 (228)
Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems [PDF]
Qualitative Theory of Dynamical Systems, 2014 Agraïments: FEDER-UNAB10-4E-378. The first and second author are supported by CAPES-MECD grant PHB-2009-0025-PC. The third author is supported by FAPESP-2010/17956-1. We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers x˙ = y(−1 + 2αx + 2βx2), y˙ = x + α(y2 − x2) +
Jaume Llibre +2 more
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Qualitative Theory of Dynamical Systems, 2020 Using the Euler-Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite ...
Jaume Llibre, Clàudìa Valls
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4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory [PDF]
International Journal of Dynamical Systems and Differential Equations, 2020 The averaging theory of second order shows that for polynomial differential systems in ℝ4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.
Amina Feddaoui +2 more
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Qualitative Theory of Dynamical Systems, 2008 In this paper we classify the global phase portraits of all reversible linear differential systems with cubic homogeneous polynomial nonlinearities defined in the plane and having a non degenerate center at the origin. The reversibility is given by a linear involution having a fixed set of dimension 1.
Claudio A. Buzzi +2 more
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Planar Cubic Polynomial Differential Systems with the Maximum Number of Invariant Straight Lines [PDF]
Rocky Mountain Journal of Mathematics, 2006 We classify all cubic systems possessing the maximum number of invariant straight lines (real or complex) taking into account their multiplicities. We prove that there are exactly 23 topological different classes of such systems. For every class we provide the configuration of its invariant straight lines in the Poincare disc.
Jaume Llibre, Nicolae Vulpe
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Configuration of planar Kolmogorov cubic polynomial differential systems with the most centers
Discrete and Continuous Dynamical Systems - B, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hongjin He, Changjian Liu, Dongmei Xiao
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On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems [PDF]
Pacific Journal of Mathematics, 2020 We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can exhibit. Moreover, we analyze the possible configurations of these centers with respect to the invariant coordinate axes, and obtain that the real algebraic curve xy(a+bx+cy+dx2+exy+fy2)=h has at most four families of level ovals in R2 for all real ...
Jaume Llibre, Dongmei Xiao
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Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2 [PDF]
Applied Mathematics and Computation, 2014 Agraïments: FEDER-UNAB-10-4E-378, and a CAPES Grant No. 88881. 030454/2013-01 from the program CSF-PVE. The second authors is partially supported by the project CAPES Grant No. 88881.030454/2013-01 from the program CSF-PVE and CNPq grant "Projeto Universal 472796/2013-5". The second author is supported by CAPES/GDU - 7500/13-0.
Jaume Llibre +2 more
+11 more sources
Centers of cubic polynomial differential systems
Communications on Pure and Applied AnalysiszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gerardo H. Anacona +2 more
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On the centers of cubic polynomial differential systems with four invariant straight lines [PDF]
Topological Methods in Nonlinear Analysis, 2020 Assume that a cubic polynomial differential system in the plane has four invariant straight lines in generic position, i.e. they are not parallel and no more than two straight lines intersect in a point. Then such a differential system only can have 0, 1 or 3 centers.
Jaume Llibre
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