Research Interests and Activities

Bruce B. Peckham


Research Overview

My research is mostly in the general area of DYNAMICAL SYSTEMS. More specifically, I study the iteration of maps and ask how the dynamical properties of the maps change as parameters in the defining equations change. This is called BIFURCATION THEORY.

Primary topics of interest:

Links:



Publications


  1. "The Closing of Resonance Horns for Periodically Forced Oscillators," Thesis, University of Minnesota, 1988.
    See abstract. See full text pdf.

  2. "The Necessity of the Hopf Bifurcation in Families of Periodically Forced Oscillators," Nonlinearity (3) , pp. 261-280, 1990.
    See abstract. Download published version from IOP Nonlinearity.

  3. "Period Doubling with Higher Order Degeneracies ," with I. G. Kevrekidis, SIAM Journal of Mathematical Analysis, Vol. 22, No. 6, pp. 1552-1574, 1991.
    See abstract. Download published version from SIAM JMA. Download reprint from Here.

  4. Picture Resonance Surfaces

  5. "Resonance Surfaces for Forced Oscillators," with R. P. McGehee, Geometry Center Research Report GCG70, Feb. 1995, and Experimental Mathematics, Vol.3, No. 3, pp. 221-244, 1994.
    See abstract.
    Download reprint from Experimental Mathematics.




  6. "Bananas and banana splits: A parametric degeneracy in the Hopf bifurcation for maps," with C. E. Frouzakis and I. G. Kevrekidis, SIAM J Math Analysis, Vol. 26, No. 1, pp. 190-217, 1995.
    See abstract. Download full text pdf preprint. Download published version from SIAM JMA.

  7. Picture Resonance Surfaces
  8. "Determining the global topology of resonance surfaces for periodically forced oscillator families" with R. P. McGehee 1992 Normal Forms and Homoclinic Chaos Conference Proceedings, Fields Institute Communications, Vol. 4, Americal Mathematical Society, pp. 233-251, 1995.
    See abstract. See full text pdf preprint.

  9. "Arnold Flames and Resonance Surface Folds" with R. P. McGehee, Geometry Center Research Report GCG84, July 1995, and International Journal of Bifurcation and Chaos, Vol. 6, No. 2 (1996) 315-336.
    See abstract.
    Download pdf text preprint (without figures). Download pdf of figures. Download published version from IJBC.





  10. "Real Perturbation of Complex Analytic Maps: Points to Regions" International Journal of Bifurcation and Chaos, Vol. 8, No. 1, (1998) 73-93.
    See abstract. See full text pdf preprint. Download published version from IJBC.


  11. "Global parametrization and computation of resonance surfaces for periodically forced oscillators" Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, E. Doedel and L. Tuckerman, Editors, IMA Volumes in Mathematics and its Applications, Vol. 119, Springer-Verlag, 385-406, 2000.
    See abstract. See full text pdf preprint.


  12. "Real Continuation from the Complex Quadratic Family: Fixed Point Bifurcation Sets" Bruce B. Peckham and James Montaldi, International Journal of Bifurcation and Chaos, Vol. 10, No. 2, 391-414, 2000.
    See abstract. View full text pdf preprint. Download published version from IJBC.

  13. "Lighting Arnold Flames: Resonance in Doubly Forced Periodic Oscillators," Bruce B. Peckham and I. G. Kevrekidis, Nonlinearity , Vol 15, No. 2, pp405--, 2002. See abstract. See full text pdf preprint. Download published version from IOP Nonlinearity.

  14. "Plant community dynamics, nutrient cycling and alternative stable equilibria in peatlands," John Pastor, Bruce Peckham, Scott Bridgham, Jake Weltzin, and Jiquan Chen, The American Naturalist, Vol. 160, No. 5, 553-568, 2002. See abstract.

  15. "A route to computational chaos revisited: noninvertibility and the breakup of an invariant circle," C. E. Frouzakis , I. G. Kevrekidis and Bruce B. Peckham, Physica D , Vol. 177, 101-121, 2003. See abstract. See full text pdf preprint or download from arXiv.org.


  16. "Computing Arnold Tongue Scenarios, Frank Schilder and Bruce Peckham Journal of Computational Physics 220 (2007), 932-951. Electronic version posted 2006. See abstract. See full text pdf preprint.

  17. "Unfolding the cusp-cusp bifurcation of planar endomorphisms," Bernd Krauskopf, Hinke Osinga and Bruce Peckham, SIAM Journal on Dynamical Systems, Vol. 6 (2), 2007, pp403-440. See abstract. See full text preprint pdf preprint. Download published version from SIADS.

  18. "A Producer-Consumer Model with Stoichiometric Elimination Mechanisms," Laura Zimmermann, Bruce Peckham, John Pastor and Harlan Stech, UMD Technical Report, 2008. See abstract. See full text pdf preprint.

  19. ``Enrichment in a general class of stoichiometric producer-consumer population growth models,'' Harlan Stech, Bruce Peckham and John Pastor, Theoretical Population Biology, Volume 81, Issue 3, 2012, 210-222. See abstract. Download fulltext preprint fulltext PDF preprint. Get published version from TPB link.

  20. ``Enrichment Effects in a Simple Stoichiometric Producer-Consumer Population Growth Model,'' Harlan Stech, Bruce Peckham and John Pastor, Communications in Applied Analysis, Vol. 16, No. 4, 2012, 687-702. See abstract. Download fulltext preprint fulltext PDF preprint.

  21. ``Quasi-equilibrium Reduction in a General Class of Stoichiometric Producer-Consumer Models,'' Harlan Stech, Bruce Peckham and John Pastor, Journal of Biological Dynamics, Volume 6, No. 2, 2012, 992-1018. See abstract. Free access to full text available at JBD link.

  22. ``Dynamics of nonholomorphic singular continuations: a case with radial symmetry," Bozyk B D and Peckham B B, International Journal of Bifurcation and Chaos, Vol. 23, No. 11, 22 pages, 2013. Journal of Difference Equations and Applications, Vol. 23, No. 11, 22 pages, 2013. See abstract. See full text pdf preprint. Download published version from IJBC.

  23. ``Classification of critical sets and their images for quadratic maps of the plane,'' C-H Nien, B B Peckham, and R P McGehee, Journal of Difference Equations and Applications, 2016. See full text pdf preprint at arXiv.org. Download published version from JDEA.


Software


  1. "To Be Continued ... " A discrete dynamical systems software package. TBC home page..

VCR Movies


  1. "Resonance City," a 15 minute video of various resonance surfaces for a periodically forced oscillator model, made with R. P. McGehee at the Geometry Center, Minneapolis, MN. For related discussion see "Resonance Surfaces for Forced Oscillators" abstract.

Acknowledgement of Support



This page (http://www.d.umn.edu/~bpeckham/www) is maintained by Bruce Peckham (bpeckham@d.umn.edu) and was last modified on Thursday, 24-Mar-2016 22:48:06 CDT.