Results 131 to 140 of about 2,258 (187)

Bifurcation of limit cycles near a heteroclinic loop with nilpotent cusps

Communications in Nonlinear Science and Numerical Simulation, 2023
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Deyue Ma, Junmin Yang
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Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation

SIAM Journal on Applied Mathematics, 1999
Summary: Homoclinic and heteroclinic bifurcations from a heteroclinic loop are considered. The system under consideration has three parameters, two of which are not suitable for generic unfoldings. Analytical criteria in terms of derivatives to Melnikov's functions are given for nongeneric parameters.
Bo Deng, Mark J. Friedman, Shui-Nee Chow
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Bifurcation of limit cycles near heteroclinic loops in near-Hamiltonian systems

Communications in Nonlinear Science and Numerical Simulation, 2020
In this paper, a method for calculating the expansion coefficients of the first order Melnikov function is proposed, which is suitable for the near-Hamiltonian system near the polycycle with hyperbolic saddles. With more those coefficients, more limit cycles could be determined around the polycycle.
Wei Geng, Yun Tian
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Codimension 3 Non-resonant Bifurcations of Rough Heteroclinic Loops with One Orbit Flip*

Chinese Annals of Mathematics, Series B, 2006
This paper presents three bifurcation theorems from a non-principal rough heteroclinic loop of a four dimensional real autonomous differential system under a perturbation of codimension \(3\). These theorems investigate the bifurcation of a heteroclinic loop, a homoclinic loop and a periodic orbit. The main tool used to state and prove these results is
Shuliang Shui, Deming Zhu
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Homoclinic Loops, Heteroclinic Cycles, and Rank One Dynamics

SIAM Journal on Applied Dynamical Systems, 2015
We prove that genuine nonuniformly hyperbolic dynamics emerge when flows in ${R}^{N}$ with homoclinic loops or heteroclinic cycles are subjected to certain time-periodic forcing. In particular, we establish the emergence of strange attractors and Sinai--Ruelle--Bowen (SRB) measures with strong statistical properties (central limit theorem, exponential ...
Anushaya Mohapatra, William Ott
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Bifurcation of rough heteroclinic loop with orbit and inclination flips

Nonlinear Analysis: Real World Applications, 2007
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Zhiqin Qiao, Qiuying Lu, Deming Zhu
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Bifurcation of limit cycles from a heteroclinic loop with two cusps

Chaos, Solitons & Fractals, 2014
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Jiao Li, Tonghua Zhang, Maoan Han
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Limit Cycles Near a Homoclinic or Heteroclinic Loop

, 2012
Chapter 8 considers bifurcation of limit cycles near a homoclinic or heteroclinic loop. The method of computing the Melnikov functions near a homoclinic or heteroclinic loop is developed and explicit formulae for the coefficients in the expansion of the Melnikov function are derived. Double homoclinic loop is also studied in this chapter.
Maoan Han, Pei Yu
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Study on limit cycles near homoclinic loops and heteroclinic loops with hyperbolic saddles

Journal of Differential Equations
In the paper, the authors study the number of limit cycles near homoclinic and heteroclinic loops of near-Hamiltonian systems with hyperbolic saddles. They provide a new algorithm to calculate the coefficients of its asymptotic expansion of the first-order Melnikov function. An example is given to demonstrate the effectiveness of the new algorithm.
Hongwei Shi, Changjian Liu, Yanqin Xiong
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Generating Grid Multiwing Chaotic Attractors by Constructing Heteroclinic Loops Into Switching Systems

IEEE Transactions on Circuits and Systems II: Express Briefs, 2011
Over the last two decades, multiwing chaos generation has seen promising advances and becomes an active research field today. It is well known that there is a gap between theoretical design and engineering applications in multiwing chaos generation. That is, most theoretical designs of multiwing chaotic attractors with mathematical proofs or numerical ...
Simin Yu, Jinhu Lü, Guanrong Chen, Xinghuo Yu   +3 more
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