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

摘要

An algorithm to detect homoclinic twist bifurcation points in Z2 -udsymmetric autonomous systems of ordinary differential equations in R4udalong curves of symmetric homoclinic orbits to hyperbolic equilibria hasudbeen developed. We show convergence of numerical approximations to homoclinicudtwist bifurcation points in such systems. A test function is definedudon the homoclinic solutions, which has a regular zero in the codimensiontwoudbifurcation points. This codimension-two singularity can be continuedudappending the test function to a three parameter vector field. We demonstrateudthe use of the test function on several examples of two coupledudJosephson junctions.