About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

Stephanus A. van Gils, V. Tchistiakov, V. Tchistiakov

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Abstract

An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversiteit Twente
Number of pages25
ISBN (Print)0169-2690
Publication statusPublished - 1997

Publication series

NameMemorandum / Faculty of Applied Mathematics
PublisherUniversity of Twente, Faculty of Applied Mathematics
No.1371

Keywords

  • METIS-141235
  • IR-30594

Cite this

van Gils, S. A., Tchistiakov, V., & Tchistiakov, V. (1997). About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. (Memorandum / Faculty of Applied Mathematics; No. 1371). Enschede: Universiteit Twente.
van Gils, Stephanus A. ; Tchistiakov, V. ; Tchistiakov, V. / About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. Enschede : Universiteit Twente, 1997. 25 p. (Memorandum / Faculty of Applied Mathematics; 1371).
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van Gils, SA, Tchistiakov, V & Tchistiakov, V 1997, About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. Memorandum / Faculty of Applied Mathematics, no. 1371, Universiteit Twente, Enschede.

About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. / van Gils, Stephanus A.; Tchistiakov, V.; Tchistiakov, V.

Enschede : Universiteit Twente, 1997. 25 p. (Memorandum / Faculty of Applied Mathematics; No. 1371).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

AU - van Gils, Stephanus A.

AU - Tchistiakov, V.

AU - Tchistiakov, V.

N1 - Memorandum fac. TW nr 1371

PY - 1997

Y1 - 1997

N2 - An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.

AB - An algorithm to detect homoclinic twist bifurcation points in Z2 - symmetric autonomous systems of ordinary differential equations in R4 along curves of symmetric homoclinic orbits to hyperbolic equilibria has been developed. We show convergence of numerical approximations to homoclinic twist bifurcation points in such systems. A test function is defined on the homoclinic solutions, which has a regular zero in the codimensiontwo bifurcation points. This codimension-two singularity can be continued appending the test function to a three parameter vector field. We demonstrate the use of the test function on several examples of two coupled Josephson junctions.

KW - METIS-141235

KW - IR-30594

M3 - Report

SN - 0169-2690

T3 - Memorandum / Faculty of Applied Mathematics

BT - About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4

PB - Universiteit Twente

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van Gils SA, Tchistiakov V, Tchistiakov V. About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. Enschede: Universiteit Twente, 1997. 25 p. (Memorandum / Faculty of Applied Mathematics; 1371).