Results 251 to 260 of about 9,183,192 (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 ...
Hebai Chen, Zhaosheng Feng, Rui Zhang 0110   +2 more
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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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Bifurcation Diagram and Global Phase Portraits of a Family of Quadratic Vector Fields in Class I

Qualitative Theory of Dynamical Systems, 2020
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Man Jia, Haibo Chen, Hebai Chen
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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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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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Classification of Global Phase Portrait of Planar Quintic Quasi-Homogeneous Coprime Polynomial Systems

Qualitative Theory of Dynamical Systems, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiu, Bao Hua, Liang, Hai Hua
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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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Global bifurcations and phase portrait of an analytically solvable nonlinear oscillator: Relaxation oscillations and saddle-node collisions

Physical Review A, 1987
A second-order nonlinear differential equation whose general solution can be expressed in terms of elementary functions is studied. Analytical expressions describing both the phase portrait and global bifurcations for all values of the parameters are given. With the advantage of being exactly solvable, this equation models essentially the same physical
Gonzalez Diego L, Piro O
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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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Symmetries in Phase Portrait

Symmetry, 2020
Yakov Krasnov
exaly