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Heteroclinic Cycles and Phase Turbulence
1999A new heteroclinic cycle is demonstrated in the case of thermal convection in a layer heated from below and rotating about a horizontal axis. This system can be realized experimentally through the use of the centrifugal force as effective gravity in the system of the rotating cylindrical annulus.
F.H. Busse, R.M. Clever
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Asymmetric Singularly Degenerate Heteroclinic Cycles
International Journal of Bifurcation and ChaosAlthough the axis-symmetric singularly degenerate heteroclinic cycles with nearby bifurcated axis-symmetric Lorenz-like attractors in axis-symmetric Lorenz-like system family were intensively studied in past decades, the scenario with asymmetric cycles has not been investigated.
Haijun Wang +3 more
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Heteroclinic Cycles and Homoclinic Closures for Generic Diffeomorphisms
Journal of Dynamics and Differential Equations, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gan, Shaobo, Wen, Lan
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Stable heteroclinic cycles for ensembles of chaotic oscillators
Physical Review E, 2002We study the formation of synchronous clusters in ensembles of globally coupled chaotic oscillators. We reveal that at least three clusters of identical synchronization are formed in such a system for large enough values of coupling strength. Our main result is an unexpected intermittent process of clusterization.
Kuznetsov, A. S. +1 more
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Noise and O(1) amplitude effects on heteroclinic cycles
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1999The dynamics of structurally stable heteroclinic cycles connecting fixed points with one-dimensional unstable manifolds under the influence of noise is analyzed. Fokker-Planck equations for the evolution of the probability distribution of trajectories near heteroclinic cycles are solved.
Stone, Emily, Armbruster, Dieter
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Asymptotic stability of heteroclinic cycles in systems with symmetry. II
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1995Systems possessing symmetries often admit robust heteroclinic cycles that persist under perturbations that respect the symmetry. In previous work, we began a systematic investigation into the asymptotic stability of such cycles. In particular, we found a sufficient condition for asymptotic stability, and we gave algebraic criteria for deciding when ...
KRUPA, M, MELBOURNE, [No Value]
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On heteroclinic cycles of competitive maps via carrying simplices
Journal of Mathematical Biology, 2015We concentrate on the effects of heteroclinic cycles and the interplay of heteroclinic attractors or repellers on the boundary of the carrying simplices for low-dimensional discrete-time competitive systems. Based on the existence of the carrying simplex for the competitive mapping, we provide the criteria on stability of the heteroclinic cycle.
Jiang, Jifa, Niu, Lei, Wang, Yi
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Heteroclinic Cycles in Symmetrically Coupled Systems
1999A characteristic feature of symmetric dynamics is the presence of robust heteroclinic cycles. Although this phenomenon was first described by dos Reis in 1978 (see [25]), it only gained wide attention in the dynamics community after the work of Guckenheimer and Holmes [18] on a dynamical system used by Busse and Clever [7] as a model of fluid ...
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Pseudo-simple heteroclinic cycles in \(\mathbb{R}^4\)
2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chossat, Pascal +2 more
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