Results 201 to 210 of about 59,907 (228)

Analytic integrability of cubic–linear planar polynomial differential systems

Journal of Differential Equations, 2015
The first author is partially supported by the MINECO/FEDER grant number MTM2014- 53703-P and the AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204.
Jaume Giné, Clàudìa Valls
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Qualitative dynamics of five quadratic polynomial differential systems exhibiting five classical cubic algebraic curves

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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Reversible Limit Cycles for Linear Plus Cubic Homogeneous Polynomial Differential System

Qualitative Theory of Dynamical Systems
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luping Wang, Yulin Zhao
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Linear estimate for the number of limit cycles of a perturbed cubic polynomial differential system

Nonlinear Analysis: Theory, Methods & Applications, 2008
In the focus of this paper is a near-Hamiltonian polynomial system in the form \[ \dot{x}=-y(a_1x+a_0)(b_1y+b_0) + \varepsilon p(x,y), \qquad \dot{y}=x(a_1x+a_0)(b_1y+b_0) + \varepsilon q(x,y), \] where \(a_0,a_1,b_0,b_1\neq0\), \(\varepsilon \geq 0\) is a small real parameter, \(p\) and \(q\) are two arbitrary polynomials of degree \(n\).
Jaume Llibre, Hao Wu, Jiang Yu
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Global $${\varvec{C}}^{\varvec{\infty }}$$ C ∞ Integrability of Cubic–Linear Polynomial Differential Systems

Qualitative Theory of Dynamical Systems, 2013
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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Centers and Lyapunov quantities in a cubic polynomial Kolmogorov differential system

Nonlinear Analysis: Real World Applications
Jaume Llibre, Zhilin Wang, Dongmei Xiao
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Bifurcations of Limit Circles and Center Conditions for a Class of Non-analytic Cubic Z2 Polynomial Differential Systems

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 ...
Feng, Li, Yi, Rong Rong, Liu Liu, Yin Yin, Lai, Jin   +7 more
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Bifurcation of Limit Cycles through Perturbing a Cubic Isochronous Center in Piecewise Polynomial Differential Systems

Qualitative Theory of Dynamical Systems
Xiuli Cen, Shangming Chen, Zhe Zhang
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Algebraic Limit Cycle of Degree 2 for Linear Type Center Plus Cubic Homogeneous Polynomial Differential Systems

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.
Luping Wang, Yuzhou Tian, Yulin Zhao
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Novel stability criteria for linear time-delay systems using Lyapunov-Krasovskii functionals with a cubic polynomial on time-varying delay

IEEE/CAA Journal of Automatica Sinica, 2021
Xian-Ming Zhang, Qing-Long Han, Xiaohua Ge   +2 more
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