Results 11 to 20 of about 13,897 (205)
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections [PDF]
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
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Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type
Electronic Journal of Qualitative Theory of Differential Equations, 2015 This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit.
Qiuying Lu, Guifeng Deng, Hua Luo
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FLIP BIFURCATION WITH RANDOM EXCITATION
Journal of Applied Analysis & Computation, 2022 Summary: In this paper, flip bifurcation with random excitation is studied by employing the methods of normal forms, Picard iterations and orthogonal polynomial approximation. For the codimension one case, a Neimark-Sacker bifurcation, a 1:2 resonance and a fold-flip bifurcation are detected.
Tang, Diandian, Ren, Jingli
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Cascades of Global Bifurcations and Chaos near a Homoclinic Flip Bifurcation: A Case Study
SIAM Journal on Applied Dynamical Systems, 2018 We study a homoclinic flip bifurcation of case~\textbf{C}, where a homoclinic orbit to a saddle equilibrium with real eigenvalues changes from being orientable to nonorientable. This bifurcation is of codimension two, and it is the lowest codimension for a homoclinic bifurcation of a real saddle to generate chaotic behavior in the form of (suspended ...
Giraldo, Andrus +2 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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THE FOLD-FLIP BIFURCATION [PDF]
International Journal of Bifurcation and Chaos, 2004 The fold-flip bifurcation occurs if a map has a fixed point with multipliers +1 and -1 simultaneously. In this paper the normal form of this singularity is calculated explicitly. Both local and global bifurcations of the unfolding are analyzed by exploring a close relationship between the derived normal form and the truncated amplitude system for the ...
Kuznetsov, Yu. A. +2 more
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Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures. [PDF]
Sci RepAhmad A +6 more
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Qualitative Theory of Dynamical Systems, 2022 Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system.
Li, Xianyi, Liu, Yuqing
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Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic balance approach [PDF]
, 1999 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS: PART
Bonani, Fabrizio, Gilli, Marco
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Discrete Dynamics in Nature and Society, 2012 A new bifurcation critical criterion of flip-Neimark-Sacker bifurcation is proposed for detecting or anticontrolling this type of codimension-two bifurcation of discrete systems in a general sense. The criterion is built on the properties of coefficients
Shengji Yao
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