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

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Gils, S.A. van and Tchistiakov, V. (1997) About convergence of numerical approximations to homoclinic twist bifurcation points in Z2-symmetric systems in R^4. [Report]

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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.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/30594
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