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Global phase portraits of the planar perpendicular problem of two fixed centers
Journal of Mathematical Physics, 2009We 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 +2 more
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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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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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Qualitative Theory of Dynamical Systems, 2016
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Qiu, Bao Hua, Liang, Hai Hua
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Qiu, Bao Hua, Liang, Hai Hua
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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
Diego L Gonzalez, Oreste Piro
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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
Diego L Gonzalez, Oreste Piro
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Nonlinear Dynamics, 2014
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Liang, Haihua +2 more
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Liang, Haihua +2 more
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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 +2 more
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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 +2 more
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Phase portrait of Hamiltonian systems with homogeneous nonlinearities
Nonlinear Analysis: Theory, Methods & Applications, 2000Armengol Gasull +2 more
exaly
Global phase portraits for a like structurally orthotropic stringer shell system
Communications in Nonlinear Science and Numerical SimulationXiuli Cen +3 more
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