Results 201 to 210 of about 3,352 (233)

Global phase portraits of planar piecewise linear refracting systems of saddle–saddle type

Nonlinear Analysis: Real World Applications, 2021
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Yi Shao, Shimin Li, Kuilin Wu
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The Classification on the Global Phase Portraits of Two-dimensional Lotka–Volterra System

Journal of Dynamics and Differential Equations, 2008
The authors present a complete classification of all quadratic planar Lotka-Volterra systems. By a very detailed investigation, they find 143 topologically inequivalent global phase portraits for these systems, up to time reversal. First, all systems with nontrivial closed orbits are examined separately.
Cao, Feng, Jiang, Jifa
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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 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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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 Piecewise Quadratic Differential Systems with a Pseudo-Center

International Journal of Bifurcation and Chaos
This paper deals with the global dynamics of planar piecewise smooth differential systems constituted by two different vector fields separated by one straight line that passes through the origin. From a quasi-canonical family of piecewise quadratic differential systems with a pseudo-focus point at the origin, which has six parameters, we investigate ...
Meriem Barkat, Rebiha Benterki, Enrique Ponce   +2 more
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Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems

Nonlinear Dynamics, 2014
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Liang, Haihua, Huang, Jianfeng, Zhao, Yulin   +2 more
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