Results 1 to 10 of about 6,100 (243)
Trans-heteroclinic bifurcation: a novel type of catastrophic shift [PDF]
Royal Society Open Science, 2018 Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth
Josep Sardanyés +2 more
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Emerging criticality at bifurcation points in heteroclinic dynamics [PDF]
Physical Review Research, 2020 Heteroclinic dynamics is a suitable framework to describe transient dynamics that is characteristic for ecological as well as neural systems, in particular for cognitive processes.
Maximilian Voit +1 more
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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 +5 more
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Stability and bifurcations of heteroclinic cycles of type Z [PDF]
Nonlinearity, 2012 Dynamical systems that are invariant under the action of a non-trivial symmetry group can possess structurally stable heteroclinic cycles. In this paper we study stability properties of a class of structurally stable heteroclinic cycles in R^n which we ...
Podvigina, Olga
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Modeling, dynamical analysis and numerical simulation of a new 3D cubic Lorenz-like system [PDF]
Scientific Reports, 2023 Little seems to be considered about the globally exponentially asymptotical stability of parabolic type equilibria and the existence of heteroclinic orbits in the Lorenz-like system with high-order nonlinear terms.
Haijun Wang +3 more
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Resonance Bifurcations of Robust Heteroclinic Networks [PDF]
SIAM Journal on Applied Dynamical Systems, 2012 46 pages, 20 figures. Supplementary material (two animated gifs) can be found on http://www.maths.leeds.ac.uk/~alastair/papers/KPR_res_net_abs ...
Alastair M. Rucklidge +2 more
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On a codimension $2$ bifurcation of heteroclinic orbits [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1987 The author proves under certain conditions the existence of a heteroclinic orbit for the perturbed equation if such heteroclinic orbit exists for the unperturbed equation. From the text: We consider a bifurcation problem of heteroclinic orbits for a family of ODEs on \(\mathbb R^n\).
Hiroshi Kokubu
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Dissecting a Resonance Wedge on Heteroclinic Bifurcations [PDF]
Journal of Statistical Physics, 2021 This article studies routes to chaos occurring within a resonance wedge for a 3-parametric family of differential equations acting on a 3-sphere. Our starting point is an autonomous vector field whose flow exhibits a weakly attracting heteroclinic network made by two 1-dimensional connections and a 2-dimensional separatrix between two equilibria with ...
Alexandre A. P. Rodrigues
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Bifurcation of heteroclinic orbits for diffeomorphisms [PDF]
Applications of Mathematics, 1991 Using the Lyapunov-Schmidt method in bifurcation theory [\textit{S. N. Chow} and \textit{J. K. Hale}, Methods of Bifurcation Theory (1982; Zbl 0487.47039)], the author investigates bifurcations of heteroclinic orbits of diffeomorphisms \(\Phi: \mathbb{R}^ 2\to \mathbb{R}^ 2\), \(\Phi(x,y)=(f(x),g(x,y))\), where \(g(x,0)\equiv0\), \(x\in(-1/2,3/2 ...
Mičhal Fĕckan
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Bifurcations of a Pair of Nonorientable Heteroclinic Cycles
Journal of Mathematical Analysis and Applications, 1998 The authors study some bifurcation problems of a pair of nonorientable heteroclinic cycles of vector fields, which are related to the study of Lorenz equations. The presence of both nonorientable cycles provides \(\Omega\)-explosion. The authors analyze what kinds of bifurcation behaviour happen for a generic two-parameter unfolding of a system with a ...
Jing Zhujun, Qi Dongwen
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