Results 251 to 260 of about 60,028 (276)

Global Phase Portraits of Separable Polynomial Rigid Systems with a Center

Journal of Nonlinear Science
The article studies separable polynomial rigid systems of the form \[ \dot{x} = -y + xH(x,y), \quad \dot{y} = x + yH(x,y), \] with \(H(x,y) = f(x)g(y)\), focusing on the case when either \(f\) or \(g\) is an odd function. This condition guarantees symmetry in the vector field, ensuring that the origin is a center and influencing the global dynamics ...
Chen, Hebai, Feng, Zhaosheng, Zhang, Rui
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Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems

Nonlinear Dynamics, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liang, Haihua, Huang, Jianfeng, Zhao, Yulin   +2 more
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Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four

Journal of Mathematical Analysis and Applications, 2020
The complete bifurcation diagram and global phase portraits in the Poincaré disc of a Lienard system of degree four with linear restoring force and three parameters are presentes. Using the rotation property, the authors find necessary and sufficient conditions for the existence of separatrix loops and limit cycles, respectively.
Chen, Xiaofeng, Chen, Hebai
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Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator

Acta Mathematicae Applicatae Sinica, English Series
This paper provides an in-depth study of the global phase portraits of uniform isochronous centers in systems of degree six, characterized by a polynomial commutator. The authors focus on systems of the form \[ \dot{x} = -y + xf(x, y) \text{ and } \dot{y} = x + yf(x, y), \] where \( f(x, y) = x\sigma(y) \), exploring the geometric implications of ...
Guo, Li-na, Chen, Ai-Yong, Zhao, Shuai-feng   +2 more
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Global Phase Portraits of Ordinary Differential Equations Modeling the Acute Promyelocytic Leukemia

Differential Equations and Dynamical Systems, 2023
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Candido, Douglas Modesto, Dias, Fabio Scalco, Mello, Luis Fernando   +2 more
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Global Phase Portraits of Memristor Oscillators

International Journal of Bifurcation and Chaos, 2014
In this paper, the global dynamics of memristor oscillators are investigated. For the sake of analysis, we first reformulate the original system into a simple form, which has only three parameters, and analyze its dynamics according to the variation of the parameters.
Chen, Hebai, Li, Xuefang
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Classification of Global Phase Portrait of Planar Quintic Quasi-Homogeneous Coprime Polynomial Systems

Qualitative Theory of Dynamical Systems, 2016
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Qiu, Bao Hua, Liang, Hai Hua
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A complete global phase portrait for the matrix Riccati equation

The 22nd IEEE Conference on Decision and Control, 1983
A complete description is given for the phase portrait of the matrix Riccati equation which arises from the optimal control and filtering problems, as well as for associated differential equations on the Grassmann and Lagrange-Grassmann manifolds. The phase portraits are characterized topologically as well as set-theoretically.
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Global phase portraits of the planar perpendicular problem of two fixed centers

Journal of Mathematical Physics, 2009
We study the global phase portrait of the classical problem of an electron in the electrostatic field of two protons that we assume fixed to symmetric distances on the x3 axis. The general problem can be formulated as an integrable Hamiltonian system of three degrees of freedom, but we restrict our study to the invariant planar case that is equidistant
Jiménez Lara, Lidia, Llibre, Jaume, Vargas, Martín   +2 more
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Global Phase Portraits for a Planar ℤ2-Equivariant Kukles Systems of Degree 3

International Journal of Bifurcation and Chaos, 2020
We provide normal forms and the global phase portraits on the Poincaré disk of all planar Kukles systems of degree [Formula: see text] with [Formula: see text]-equivariant symmetry. Moreover, we also provide the bifurcation diagrams for these global phase portraits.
Fabio Scalco Dias, Ronisio Moises Ribeiro, Claudia Valls   +2 more
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