Subordinate Sil'nikov bifurcations near some singularities of vector fields having low codimension
Hendrik Broer,Gert Vegter +1 more
TLDR
A specific singularity of a vector field on R 3 is considered in this article, of codimension 2 in the dissipative case and of codeimension 1 in the conservative case.Abstract:
A specific singularity of a vector field on R 3 is considered, of codimension 2 in the dissipative case and of codimension 1 in the conservative case. In both contexts in generic unfoldings the existence is proved of subordinate Sil'nikov bifurcations, which have codimension 1. Special attention is paid to the C°°-flatness of this subordinate phenomenon.read more
Citations
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New features of the software MatCont for bifurcation analysis of dynamical systems
TL;DR: Software issues that are in practice important for many users, e.g. how to define a new system starting from an existing one, how to import and export data, system descriptions, and computed results are discussed.
Journal ArticleDOI
Local and global behavior near homoclinic orbits
Paul Glendinning,Colin Sparrow +1 more
TL;DR: In this paper, the local behavior of systems near homoclinic orbits to stationary points of saddle-focus type is studied, with the help of numerical examples, and the results relate to global patterns of bifurcations.
Book ChapterDOI
Homoclinic and heteroclinic bifurcations in vector fields
Ale Jan Homburg,Björn Sandstede +1 more
TL;DR: An overview of homoclinic and heteroclincic bifurcation theory for autonomous vector fields is given in this article, where the main analytic and geometric techniques such as Lin's method, Shil'nikov variables, and center manifolds are discussed.
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Bifurcations and strange attractors in the Lorenz-84 climate model with seasonal forcing
TL;DR: In this article, a low-dimensional model of general circulation of the atmosphere is investigated, where the differential equations are subject to periodic forcing, and a three-dimensional Poincare mapping depends on three control parameters F, G, and, the latter being the relative amplitude of the oscillating part of the forcing.
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Transport in 3D volume-preserving flows
TL;DR: In this paper, the role of the skeleton formed by the equilibrium points, selected hyperbolic periodic orbits and cantori and connecting orbits is discussed, to which many surfaces of locally minimal flux can be attached.
References
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Foundations of mechanics
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.
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Applications of Centre Manifold Theory
TL;DR: In this paper, the authors present an approach for solving the panel flutter problem using a Second Order Equation (SOPE) and a Semigroup Theory. But their approach is limited to the case when the case is 1 < 0 and the case where 0 < 0.
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Singularities of vector fields
TL;DR: In this paper, the authors present a set of conditions générales d'utilisation of systématiques, i.e., the copie ou impression of a fichier do not contenir the présente mention de copyright.
Journal ArticleDOI
A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type
TL;DR: In this article, it was shown that in a neighborhood of a trajectory which is doubly asymptotic to a rough state of equilibrium of saddle-focus type, under addition assumptions on the dynamical system, there exists a subsystem whose trajectories are in one-to-one correspondence with a set which is the quotient space of a topological Bernoulli process with an infinite set of symbols.