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Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues [PDF]

The Scientific World Journal, 2014
By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the ...
Yinlai Jin, Xiaowei Zhu, Zheng Guo, Han Xu, Liqun Zhang, Benyan Ding   +5 more
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Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria [PDF]

The Scientific World Journal, 2014
The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Exploring Limit Cycle Bifurcations in the Presence of a Generalized Heteroclinic Loop [PDF]

Mathematics, 2023
This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m.
Erli Zhang, Stanford Shateyi
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Persistence of the heteroclinic loop under periodic perturbation

Electronic Research Archive, 2023
We consider an autonomous ordinary differential equation that admits a heteroclinic loop. The unperturbed heteroclinic loop consists of two degenerate heteroclinic orbits $ \gamma_1 $ and $ \gamma_2 $.
Bin Long, Shanshan Xu
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Sharp Bound of the Number of Zeros for a Liénard System with a Heteroclinic Loop [PDF]

Discrete Dynamics in Nature and Society, 2021
In the presented paper, the Abelian integral Ih of a Liénard system is investigated, with a heteroclinic loop passing through a nilpotent saddle. By using a new algebraic criterion, we try to find the least upper bound of the number of limit cycles ...
Junning Cai, Minzhi Wei, Guoping Pang
doaj   +3 more sources

Heteroclinic loops leading to hyperchaos [PDF]

Journal de Physique Lettres, 1985
Some homoclinic orbits and heteroclinic loops are discussed as mechanisms leading to hyperchaos.
Paul Glendinning, C. Tresser
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BIFURCATIONS OF TWISTED FINE HETEROCLINIC LOOP FOR HIGH-DIMENSIONAL SYSTEMS

Journal of Applied Analysis & Computation, 2023
Summary: In the paper, under twisted conditions, we consider the bifurcation problem of the fine heteroclinic loop with two hyperbolic critical points for high-dimensional systems. By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits as the local coordinate system in the small ...
Yinlai Jin, Dongmei Zhang, Ningning Wang, Deming Zhu   +3 more
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Bifurcations of heteroclinic loops with nonresonant eigenvalues

Journal of Mathematics and Computer Science, 2017
Summary: In this paper, we use the way of local coordinates instead of the Floquet method to study the problems of homoclinic and periodic orbits bifurcated from heteroclinic loop for high-dimensional system. Under some transversal conditions and the non-twisted or twisted conditions, we discuss the existence, uniqueness, coexistence, and non ...
Zheng Guo, Yinlai Jin, Yuerang Gao, Dandan Xie   +3 more
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Periodic or homoclinic orbit bifurcated from a heteroclinic loop for high-dimensional systems

Open Mathematics
Consider an autonomous ordinary differential equation in Rn{{\mathbb{R}}}^{n}, which has a heteroclinic loop. Assume that the heteroclinic loop consists of two degenerate heteroclinic orbits γ1{\gamma }_{1}, γ2{\gamma }_{2} and two saddle points with ...
Long Bin, Yang Yiying
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Bifurcations of a nongeneric heteroclinic loop with nonhyperbolic equilibria

Discrete & Continuous Dynamical Systems - B, 2012
In this paper, using the local moving frame approach, we investigate bifurcations of nongeneric heteroclinic loop with a nonhyperbolic equilibrium $p_1$ and a hyperbolic saddle $p_2$, where $p_1$ is assumed to undergo a transcritical bifurcation.
Fengjie Geng, Junfang Zhao, Deming Zhu, Weipeng Zhang   +3 more
openalex   +3 more sources