### Abstract

An algorithm to detect homoclinic twist bifurcation points in Z

_{2}-symmetric autonomous systems of ordinary differential equations in ℝ^{4}along curves of symmetric homoclinic orbits to hyperbolic equilibria hasbeen developed. We show convergence of numerical approximations to homoclinictwist bifurcation points in such systems. A test function is definedon the homoclinic solutions, which has a regular zero in the codimensiontwobifurcation points. This codimension-two singularity can be continuedappending the test function to a three parameter vector field. We demonstratethe use of the test function on several examples of two coupledJosephson junctions.Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente |

Number of pages | 25 |

Publication status | Published - 1997 |

### Publication series

Name | Memorandum |
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Publisher | University of Twente, Faculty of Applied Mathematics |

No. | 1371 |

ISSN (Print) | 0169-2690 |

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## Cite this

van Gils, S. A., & Tchistiakov, V. (1997).

*About Convergence of Numerical Approximations to Homoclinic Twist Bifurcation Points in Z*. (Memorandum; No. 1371). Enschede: University of Twente._{2}-Symmetric Systems in ℝ^{4}