Results 181 to 190 of about 3,877 (218)

Limit Cycles Near Homoclinic and Heteroclinic Loops

Journal of Dynamics and Differential Equations, 2008
The paper deals with a near-Hamiltonian system in the form of \[ \dot{x}=H_y + \varepsilon p(x,y,\varepsilon,\delta), \quad \dot{y}=-H_x + \varepsilon q(x,y,\varepsilon,\delta), \] where \(H(x,y)\), \(p\) and \(q\) are analytic functions in \((x,y)\in \mathbb{R}^2\), and \(p\) and \(q\) being \(C^1\) in a small real parameter \(\varepsilon \geq 0\), \(\
Han, Maoan, Yang, Junmin, Tarţa, Alexandrina-Alina, Gao, Yang   +3 more
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A competition between heteroclinic cycles

Nonlinearity, 1994
This paper analyzes the dynamics of a particular family of ordinary differential equations in \(\mathbb{R}^ 4\) that possess a high degree of symmetry. Because of the symmetry there can be structurally stable configuration of 4 equilibria, \(p\), \(q\), \(r_ 1\) and \(r_ 2\) such that there are two heteroclinic cycles of the form \(C_ i = p \to q \to ...
Kirk, Vivien, Silber, Mary
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Stationary bifurcation to limit cycles and heteroclinic cycles

Nonlinearity, 1991
The authors consider one-parametric vector fields which are equivariant under the action of the group \(\Gamma=\mathbb{Z}_ 4\cdot\mathbb{Z}^ 4_ 2\) (semi-direct product). It is supposed that \(\mathbb{R}^ 4\) is the absolutely irreducible space for \(\Gamma\). Thus the considered vector field is a perturbation of the field of the form \(\lambda x+Q(x)\)
Field, Mike, Swift, James W.
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Heteroclinic cycles in the repressilator model

Chaos, Solitons & Fractals, 2012
Abstract A repressilator is a synthetic regulatory network that produces self-sustained oscillations. We analyze the evolution of the oscillatory solution in the repressilator model. We have established a connection between the evolution of the oscillatory solution and formation of a heteroclinic cycle at infinity.
A. Kuznetsov, V. Afraimovich
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Heteroclinic Cycles and Segregation Distortion

Journal of Theoretical Biology, 1996
Abstract Segregation Distorters are genetic elements that disturb the meiotic segregation of heterozygous genotypes. The corresponding genes are “ultra-selfish” in that they force their own spreading in the population without contributing positively to the fitness of the organisms carrying them.
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Heteroclinic Cycles and Phase Turbulence

1999
A 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 Chaos
Although 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, Jun Pan, Feiyu Hu, Guiyao Ke   +3 more
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Heteroclinic Cycles and Homoclinic Closures for Generic Diffeomorphisms

Journal of Dynamics and Differential Equations, 2003
zbMATH 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, 2002
We 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., Kurths, Jürgen (Prof. Dr.)   +1 more
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Noise and O(1) amplitude effects on heteroclinic cycles

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1999
The 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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