Results 11 to 20 of about 95,578 (255)
Invariant algebraic curves for Liénard dynamical systems revisited [PDF]
Applied Mathematics Letters, 2018 A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of irreducible invariant algebraic curves for Li nard dynamical systems $x_t=y$, $y_t=-g(x)y-f(x)$ with $\text{deg} f=\text{deg} g+1$ is obtained.
Maria Demina
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Multiplicity of invariant algebraic curves in polynomial vector fields [PDF]
Pacific Journal of Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christopher, Colin +2 more
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Invariant algebraic curves for certain generalized Liénard differential system
Communications on Pure and Applied Analysis, 2023 In this work we solve the problem of finding the invariant algebraic curves of a generalized Li´enard differential system ˙x = y, ˙y = −f(x)y − g(x), where deg f = m and deg g = n and with n = m + 1, generalizing the known previous examples. In particular it is studied the case m = 3 and n = 4.
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Non-algebraic invariant curves for polynomial planar vector fields
Discrete & Continuous Dynamical Systems - A, 2004 The authors develop a constructive method to search for nonalgebraic invariant curves \(f(x,y)=0\) for planar polynomial differential equations \(\dot x=P(x,y),\, \dot y=Q(x,y).\) More concretely, they search for functions \(f\) of the form \(f(x,y)=\sum_{k=\ell}^n f_k(x,y)=0\) which satisfy \[ P(x,y)\partial f(x,y)/\partial x +Q(x,y)\partial f(x,y ...
García, Isaac A., Giné, Jaume
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Algebraic invariant curves and the integrability of polynomial systems
Applied Mathematics Letters, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kooij, Robert E., Christopher, Colin J.
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Invariant algebraic curves of large degree for quadratic system
Journal of Mathematical Analysis and Applications, 2005 This paper presents several interesting examples of quadratic systems (QS) having invariant algebraic curves of large degree. These examples are: (i) QS having algebraic limit cycles of degree 5 and 6; (ii) QS having algebraic saddle loops of degree 3 and 5 surrounding a strong focus; (iii) the QS, \(\dot x=1+x^2+xy,\,\) \(\dot y=57/2-81/2x^2+3y^2 ...
Christopher, Colin +2 more
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Invariant algebraic surfaces of a chronic wasting disease model
上海师范大学学报. 自然科学版, 2021 In this paper we study a chronic wasting disease (CWD) model of three dimensional ordinary differential equations. We use the method of characteristic curves to give a complete classification of this system with invariant algebraic surfaces. In addition,
YANG Yang, XIE Feng
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Explicit travelling waves and invariant algebraic curves
Nonlinearity, 2015 In this paper we introduce a precise definition of algebraic traveling wave solution for general n-th order partial differential equations. All examples of explicit traveling waves known by the authors fall in this category. Our main result proves that algebraic traveling waves exist if and only if an associated n- dimensional first order ordinary ...
Gasull, Armengol, Giacomini, Hector
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Geometry and integrability of quadratic systems with invariant hyperbolas
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Let QSH be the family of non-degenerate planar quadratic differential systems possessing an invariant hyperbola. We study this class from the viewpoint of integrability.
Regilene Oliveira +2 more
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Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams [PDF]
, 2015 This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus
Hauenstein, Jonathan D. +3 more
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