About Convergence of Numerical Approximations to Homoclinic Twist Bifurcation Points in Z₂-Symmetric Systems in ℝ⁴

An algorithm to detect homoclinic twist bifurcation points in Z₂-symmetric autonomous systems of ordinary differential equations in ℝ⁴along 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.