Results 141 to 150 of about 2,258 (187)

Bifurcations of nontwisted heteroclinic loop

Science in China Series A: Mathematics, 2000
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Tian, Qingping, Zhu, Deming
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Bifurcations of heteroclinic loops

Science in China Series A: Mathematics, 1998
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Zhu, Deming, Xia, Zhihong
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Limit Cycles Near Homoclinic and Heteroclinic Loops

Journal of Dynamics and Differential Equations, 2008
The paper deals with a near-Hamiltonian system in the form of \[ \dot{x}=H_y + \varepsilon p(x,y,\varepsilon,\delta), \quad \dot{y}=-H_x + \varepsilon q(x,y,\varepsilon,\delta), \] where \(H(x,y)\), \(p\) and \(q\) are analytic functions in \((x,y)\in \mathbb{R}^2\), and \(p\) and \(q\) being \(C^1\) in a small real parameter \(\varepsilon \geq 0\), \(\
Han, Maoan, Yang, Junmin, Tarţa, Alexandrina-Alina, Gao, Yang   +3 more
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Bifurcations of rough heteroclinic loop with two saddle points

Science in China Series A, 2003
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Jin, Yinlai, Zhu, Deming
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Bifurcations of twisted heteroclinic loop with resonant eigenvalues

Nonlinear Dynamics, 2018
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Yinlai Jin, Xiaowei Zhu, Yuanyuan Liu, Han Xu, Nana Zhang   +4 more
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Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation

Nonlinear Dynamics, 2012
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Geng, Fengjie, Xu, Yancong
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Limit Cycle Bifurcations Near a Heteroclinic Loop with Two Nilpotent Cusps of General Order

International Journal of Bifurcation and Chaos, 2022
In this paper, we study the expansion of the first order Melnikov function near a heteroclinic loop with two nilpotent cusps of general order. More precisely, the order of the two cusps is [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] [Formula: see text]. For general [Formula: see text] and [Formula: see text], we
Junmin Yang, Xing Hu
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Heteroclinic bifurcation near a loop tangent to an invariant line

Journal of Differential Equations
Xianbo Sun, Guilin Ji, Qun Bin
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Limit Cycles Near a Centre and a Heteroclinic Loop in a Near–Hamiltonian Differential System

Journal of Dynamics and Differential Equations, 2022
The authors obtain a more accurate expression of the third coefficient in the asymptotic expansion of the first order Melnikov function near a polycycle with hyperbolic saddles for an analytic near-Hamiltonian system without a prescribed form of the Hamiltonian, and characterize its higher order coefficients and establish the results on limit cycle ...
Lijun Wei, Xiang Zhang, Jinbo Zhu
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Bifurcation of limit cycles from a heteroclinic loop with a cusp

Nonlinear Analysis: Theory, Methods & Applications, 2011
Bifurcation of limit cycles is studied by investigating the expansion of the first Melnikov function of a near-Hamiltonian system \[ x' = H_y +\varepsilon p(x, y, \delta),\quad y' = -H_x +\varepsilon q(x, y, \delta) \] near a heteroclinic loop with a cusp and a saddle or two cusps. Using the formulae obtained for computing the first coefficients of the
Sun, Xianbo, Han, Maoan, Yang, Junmin
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