About convergence of numerical approximations to homoclinic twist bifurcation points in Z 2 - symmetric systems in R 4
نویسنده
چکیده
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.
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