Results 1 to 10 of about 180,188 (276)
Imperfect Homoclinic Bifurcations [PDF]
Physical Review E, 2001 Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations.
A. Arnéodo +23 more
core +3 more sources
Bifurcations of cubic homoclinic tangencies in two-dimensional\n symplectic maps [PDF]
, 2016 We study bifurcations of cubic homoclinic tangencies in two-dimensional symplectic maps. We distinguish two types of cubic homoclinic tangencies, and each type gives different first return maps derived to diverse conservative cubic H\'enon maps with ...
Marina Gonchenko +2 more
core +4 more sources
Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation [PDF]
Abstract and Applied Analysis, 2014 The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
doaj +4 more sources
Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations [PDF]
SIAM Journal on Applied Dynamical Systems, 2015 The Koper model is a three-dimensional vector field that was developed to study complex electrochemical oscillations arising in a diffusion process.
Guckenheimer, John, Lizarraga, Ian
core +2 more sources
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
doaj +2 more sources
Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field in R4 [PDF]
Discrete Dynamics in Nature and Society, 2015 We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field in R4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of ...
Tiansi Zhang, Dianli Zhao
doaj +2 more sources
Comparison of Homoclinic Bifurcations Between Grid-Following and Grid-Forming Converters
IEEE transactions on industrial electronics (1982. Print), 2023 A second-order model is developed to describe the essential behavior of the grid-following converter (GFLC) and the grid-forming converter (GFMC) for studying the synchronization characteristics of grid-connected converter systems.
Jingxi Yang +5 more
openalex +3 more sources
Pattern dynamics near inverse homoclinic bifurcation in fluids [PDF]
Physical review. E, Statistical, nonlinear, and soft matter physics, 2013 We report for the first time the pattern dynamics in the vicinity of an inverse homoclinic bifurcation in an extended dissipative system. We observe, in direct numerical simulations of three dimensional Rayleigh-Bénard convection, a spontaneous breaking ...
Pinaki Pal +3 more
semanticscholar +4 more sources
Resonance bifurcation from homoclinic cycles
Journal of Differential Equations, 2009 Consider a dynamical system \(x' = f(x)\) in \(\mathbb{R}^n\), and a group \(G\) (in this case a finite group) acting in \(\mathbb{R}^n\) through a linear representation. The dynamnical system is \(G\)-symmetric if \(f (g x) = g f(x)\) for all \(x\) and all \(g \in G\).
R. Driesse, Ale Jan Homburg
openalex +6 more sources
Bifurcations of planar sliding homoclinics [PDF]
Mathematical Problems in Engineering, 2006 We study bifurcations from sliding homoclinic solutions to bounded solutions on ℝ for certain discontinuous planar systems under periodic perturbations. Sufficient conditions are derived for such perturbation problems.
Jan Awrejcewicz +2 more
openalex +3 more sources