### Abstract

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. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained.

Original language | English (US) |
---|---|

Pages (from-to) | 499-506 |

Number of pages | 8 |

Journal | Chaos |

Volume | 9 |

Issue number | 2 |

State | Published - Jun 1999 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Chaos*,

*9*(2), 499-506.

**Noise and O(1) amplitude effects on heteroclinic cycles.** / Stone, Emily; Armbruster, Hans.

Research output: Contribution to journal › Article

*Chaos*, vol. 9, no. 2, pp. 499-506.

}

TY - JOUR

T1 - Noise and O(1) amplitude effects on heteroclinic cycles

AU - Stone, Emily

AU - Armbruster, Hans

PY - 1999/6

Y1 - 1999/6

N2 - 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. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained.

AB - 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. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained.

UR - http://www.scopus.com/inward/record.url?scp=0001064987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001064987&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001064987

VL - 9

SP - 499

EP - 506

JO - Chaos (Woodbury, N.Y.)

JF - Chaos (Woodbury, N.Y.)

SN - 1054-1500

IS - 2

ER -