Results 161 to 170 of about 648 (183)

Robust Heteroclinic Cycles

Applied Mathematics and Optimization, 1997
A heteroclinic cycle in a dynamical system is given by a finite cyclic sequence of trajectories each connecting two fixed points. Robustness means that a cycle nearby still exists after perturbing the system in a particular admissible way. Here, one allows for a stable state with high symmetry to lose its stability and some of its symmetry.
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Structurally stable heteroclinic cycles

Mathematical Proceedings of the Cambridge Philosophical Society, 1988
This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of Cr vector fields equivariant with respect to a symmetry group. In the space X(M) of Cr vector fields on a manifold M, there is a residual set of vector fields having no ...
Guckenheimer, John, Holmes, Philip
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Homoclinic and Heteroclinic Bifurcations Close to a Twisted Heteroclinic Cycle

International Journal of Bifurcation and Chaos, 1998
We study the interaction of a transcritical (or saddle-node) bifurcation with a codimension-0/codimension-2 heteroclinic cycle close to (but away from) the local bifurcation point. The study is motivated by numerical observations on the traveling wave ODE of a reaction–diffusion equation.
Zimmermann, Martín G., Natiello, Mario A.   +1 more
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Heteroclinic cycles and wreath product symmetries

Dynamics and Stability of Systems, 2000
We consider the existence and stability of heteroclinic cycles arising by local bifurcation in dynamical systems with wreath product symmetry = Z 2 G, where Z 2 acts by - 1 on R and G is a transitive subgroup of the permutation group S N (thus G has degree N). The group acts absolutely irreducibly on R N .
ANA PAULA S. DIAS, BENOIT DIONNE, IAN STEWART   +2 more
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Heteroclinic Cycles in Nature

Izvestiya, Physics of the Solid Earth, 2020
Heteroclinic cycle is an invariant of a dynamical system comprised of steady states (or more general invariant subsets) and heteroclinic trajectories. The behavior of a dynamical system with a heteroclinic cycle is intermittent: a typical trajectory stays for a long time close to a steady state while the transitions between the states occur much faster.
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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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