BibTeX
@INCOLLECTION{
         Phipps2005POo,
       author = "Eric Phipps and Richard Casey and John Guckenheimer",
       title = "Periodic Orbits of Hybrid Systems and Parameter Estimation via {AD}",
       editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
         Norris",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       year = "2005",
       abstract = "Periodic processes are ubiquitous in biological systems, yet modeling these
         processes with high fidelity as periodic orbits of dynamical systems is challenging. Moreover,
         mathematical models of biological processes frequently contain many poorly-known parameters. This
         paper describes techniques for computing periodic orbits in systems of hybrid differential-algebraic
         equations and parameter estimation methods for fitting these orbits to data. These techniques make
         extensive use of automatic differentiation to evaluate derivatives accurately and efficiently for
         time integration, parameter sensitivities, root finding and optimization. The resulting algorithms
         allow periodic orbits to be computed to high accuracy using coarse discretizations. Derivative
         computations are carried out using a new automatic differentiation package called ADMC++ that
         provides derivatives and Taylor series coefficients of matrix-valued functions written in the Matlab
         programming language. The algorithms are applied to a periodic orbit problem in rigid-body dynamics
         and a parameter estimation problem in neural oscillations.",
       crossref = "Bucker2005ADA",
       ad_tools = "ADMC++",
       pages = "211--223",
       doi = "10.1007/3-540-28438-9_19"
}