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Rendiconti del Circolo Matematico di Palermo Series 2, 2021
The object of study in this paper is the set of quadratic differential systems on \(\mathbb{R}^2\). The authors propose the study of five subfamilies which have different types of polynomial cubic first integrals. The authors provide the systems (which may depend on some parameters), the corresponding first integrals and the required cofactors.
Ahlam Belfar, Rebiha Benterki
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The object of study in this paper is the set of quadratic differential systems on \(\mathbb{R}^2\). The authors propose the study of five subfamilies which have different types of polynomial cubic first integrals. The authors provide the systems (which may depend on some parameters), the corresponding first integrals and the required cofactors.
Ahlam Belfar, Rebiha Benterki
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Qualitative Theory of Dynamical Systems, 2014
The cubic–linear polynomial differential systems having at least one finite singularity are affine equivalent to the systems of the form $$\begin{aligned} \begin{array}{l} x'=P(x,y)=bx+cy+dx^{2}+exy+fy^{2}+gx^{3}+hx^{2}y+ixy^{2}+jy^{3},\\ y'=Q(x,y), \end{array} \end{aligned}$$ with \(g^2+h^2+i^2+j^2\ne 0\) (otherwise it is quadratic–linear), and
Yangyou Pan, Cong Wang, Xiang Zhang
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The cubic–linear polynomial differential systems having at least one finite singularity are affine equivalent to the systems of the form $$\begin{aligned} \begin{array}{l} x'=P(x,y)=bx+cy+dx^{2}+exy+fy^{2}+gx^{3}+hx^{2}y+ixy^{2}+jy^{3},\\ y'=Q(x,y), \end{array} \end{aligned}$$ with \(g^2+h^2+i^2+j^2\ne 0\) (otherwise it is quadratic–linear), and
Yangyou Pan, Cong Wang, Xiang Zhang
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Reversible Limit Cycles for Linear Plus Cubic Homogeneous Polynomial Differential System
Qualitative Theory of Dynamical SystemszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Luping, Zhao, Yulin
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Acta Mathematica Sinica, English Series, 2012
The system (1), \[ \begin{multlined} {dx\over dt}= -y+ {d+1\over 2} x^4 y+ (3B_{03}+ B_{12}- 3B_{03} d- B_{12} d) x^3 y^2+ (-\textstyle{{1\over 2}}- 14A_{03}- 4A_{12}+\\ +\textstyle{{1\over 2}} d+ 2A_{03} d) x^2 y^3+ (B_{12}- B_{03} d- B_{12}d) xy^4+ (-1-4A_{03}- 4A_{12}) y^5,\end{multlined} \] \[ \begin{multlined} {dy\over dt}= x- x^5+ (12A_{03 ...
Li, Feng, Liu, Yi Rong, Jin, Yin Lai
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The system (1), \[ \begin{multlined} {dx\over dt}= -y+ {d+1\over 2} x^4 y+ (3B_{03}+ B_{12}- 3B_{03} d- B_{12} d) x^3 y^2+ (-\textstyle{{1\over 2}}- 14A_{03}- 4A_{12}+\\ +\textstyle{{1\over 2}} d+ 2A_{03} d) x^2 y^3+ (B_{12}- B_{03} d- B_{12}d) xy^4+ (-1-4A_{03}- 4A_{12}) y^5,\end{multlined} \] \[ \begin{multlined} {dy\over dt}= x- x^5+ (12A_{03 ...
Li, Feng, Liu, Yi Rong, Jin, Yin Lai
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Journal of Dynamical and Control Systems
A system of two ordinary nonlinear autonomous differential equations is considered, the linear approximation matrix of which has eigenvalues \(i\) and \(-i\). The nonlinear parts of the equations are binary forms of the third degree with real coefficients.
Wang, Luping, Tian, Yuzhou, Zhao, Yulin
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A system of two ordinary nonlinear autonomous differential equations is considered, the linear approximation matrix of which has eigenvalues \(i\) and \(-i\). The nonlinear parts of the equations are binary forms of the third degree with real coefficients.
Wang, Luping, Tian, Yuzhou, Zhao, Yulin
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Centers and Lyapunov quantities in a cubic polynomial Kolmogorov differential system
Nonlinear Analysis: Real World ApplicationsJaume Llibre, Zhilin Wang, Dongmei Xiao
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Hypercalcemia and cancer: Differential diagnosis and treatment
Ca-A Cancer Journal for Clinicians, 2018Sarah B Fisher, Nancy D Perrier, Facs
exaly
On the number of limit cycles of a perturbed cubic polynomial differential center
Journal of Mathematical Analysis and Applications, 2013Shimin Li, Yulin Zhao
exaly