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Normal Forms of Planar Polynomial Differential Systems
Qualitative Theory of Dynamical Systems, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abderrahmane Turqui, Dahira Dali
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Polynomial differential systems with hyperbolic limit cycles
Journal of Geometry and Physics, 2023One of the main problems of the qualitative theory of the planar differential equations is the study their limit cycles. In this paper given an algebraic curve of degree n we characterize the planar polynomial differential systems of degree greater or equal than n which admit the ovals of the algebraic curve as hyperbolic limit cycles.
Llibre, Jaume, Valls, Clàudia
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Decomposition of Reflexive Differential-Difference Polynomial Systems
Applied Mechanics and Materials, 2013This paper presents a zero decomposition algorithm for reflexive difference and differential polynomial systems. The problem of negative exponent of difference operators in DD-polynomials is solved by means of generalized term order. Our algorithm would be used to decompose the zero set of a finitely generated reflexive DD-polynomial set into the union
Zhi Wang Gan, Meng Zhou
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Center conditions for a polynomial differential system
Differential Equations, 2013The authors obtain 16 center conditions for a polynomial differential system with 27 parameters.
Sadovskii, A. P., Shcheglova, T. V.
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TOTALLY BOUNDED DIFFERENTIAL POLYNOMIAL SYSTEMS
2002Properties of totally bounded polynomial systems are analyzed and bifurcations are ...
CONTI, ROBERTO, GALEOTTI, MARCELLO
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Dynamical equivalence and unbounded polynomial differential systems
Nonlinear Analysis: Theory, Methods & Applications, 1988Summary: Autonomous systems of ordinary differential equations are said to be dynamically equivalent if there is a homeomorphism of their phase spaces mapping each solution of one system into a solution of the other. Dynamical equivalence conserves the time of motion of trajectories as well as the trajectories, while topological equivalence need only ...
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Boundedness and unboundedness in polynomial differential systems
Nonlinear Analysis: Theory, Methods & Applications, 1984A differential system is bounded if all of its solutions are bounded [as time increases], unbounded if there is an unbounded solution. Suppose x is an n-vector, H(x) is a homogeneous vector polynomial, P(x) is a polynomial of lower degree. The boundedness or unboundedness of the polynomial system (1), \(x'=P(x)+H(x)\), can be determined by the type ...
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Limit Cycles for a Discontinuous Quintic Polynomial Differential System
Qualitative Theory of Dynamical Systems, 2019This paper studies the maximum number of limit cycles that bifurcate from a periodic annulus for a discontinuous quintic differential system. Using the first-order averaging method, the author proves that 8 is a lower bound of the maximum number and 10 is an upper bound.
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