Computing periodic orbits with high accuracy Original Research Article

This paper introduces a new family of algorithms for computing periodic orbits of vector fields. These global methods achieve high accuracy with relatively coarse discretizations of periodic orbits through the use of automatic differentiation. High degree Taylor series expansions of trajectories are computed at mesh points. On a fixed mesh, we construct closed curves that converge smoothly to periodic orbits as the degree of the Taylor series expansions increase. The algorithms have been implemented in Matlab together with the use of the automatic differentiation code ADOL-C. Numerical tests of our codes are compared with AUTO calculations using the Hodgkin-Huxley equations as a test problem.