Evelyn Sander

Business Address:
Department of Mathematical Sciences
George Mason University, MS 3F2
4400 University Drive
Fairfax, VA 22030

Work Phone: (703) 993-1490
Fax: (703) 993-1491
E-mail: esander @
Home Page:

Northwestern University, B.A, 1990, Honors, Phi Beta Kappa
University of Minnesota, Ph.D., 1996, R. McGehee, advisor.
Employment History:
1990-92 Teaching assistant, School of Mathematics, University of Minnesota.
1993-95 Employed as a mathematical writer, the Geometry Forum, an NSF funded Web site.
1994-96 Employed for curriculum development and teaching, the Geometry Center, University of Minnesota.
1996-98 Postdoctoral fellowship, Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology.
1998-2000 Visiting assistant professor, George Mason University.
2000-2005 Assistant professor, George Mason University.
2005- Member of the Center for Neural Dynamics, Krasnow Institute.
2005-2012 Associate professor, George Mason University.
August 25, 2012 - Professor, George Mason University.

Grants, Fellowships, and Awards:
1991, 1992, 1994 summer fellowship, School of Mathematics, University of Minnesota.
1995-96 Louise T. Dosdall Graduate fellowship, University of Minnesota.
January, 1999 Association for Women in Mathematics travel grant.
August, 2000 National Science Foundation travel grant.
Spring, 2002 College of Arts and Sciences Junior Faculty Awards in the Social Sciences and Sciences for "Noninvertibility in Biological Models."
Summer, 2002 Summer Research Support for Tenure Track Faculty for "Starchy Gels, Sea Shells, and Animal Coats."
January 1, 2004- December 31, 2006 "A dynamical framework for transient neuronal patterns" (Principal Investigator) NIH-NIMH Grant Number R03-MH67659, $140,569.
September 1, 2006-August 31, 2010 "Mechanisms of wave propagation in neuronal tissue" (co-PI) CRCNS grant, NIH-NIMH Grant Number R01-MH79502, $1,269,896.
September 1, 2006-August 31, 2013, Undergraduate research in computational mathematics (co-PI), CSUMS, NSF Grant Number DMS-0639300, $1,057,257.
August 15, 2009 - July 31, 2013 "A Hybrid of Theoretical and Computational Methods for Bifurcation Analysis" (co-PI) NSF Grant Number DMS-0907818, $105,000.
2010-11, COS Publication Award.
September 2012-January 2013 Long Term Visitor, Infinite Dimensional and Stochastic Dynamical Systems and Their Applications, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis.
Fall 2014, IBM Visiting Professor, Applied Math, Brown University.
January 2014 - June 30, 2014, "Calculus-based STEM learning through the arts," Mason 4-VA Innovation Grant, $20,000.
July 2014, Travel Grant, Association for Women in Mathematics, $1736.
July 1, 2014 - June 30, 2017, "EXTREEMS-QED: Undergraduate Research in Computational and Data-Enabled Mathematics" (co-PI), NSF Grant Number DMS-1407087 $599,885.

Research Interests: My research is on numerical and theoretical methods of dynamical systems. I have done work studying global bifurcations for one-, two, and three-dimensional diffeomorphisms, and finite dimensional noninvertible maps and relations. I also study ordinary, partial, and delay differential equations modeling pattern formation in materials science, chemistry, neuroscience, and biology. This includes biological and chemical systems modeled by reaction-diffusion equations with Turing instabilities, the process of spinodal decomposition in binary and ternary metal alloys modeled by the Cahn-Hilliard equation, and phase separation in block copolymers. It also includes period-doubling cascades during the onset of complex behavior in Poincare sections of ordinary and delay differential equations.

Mathematical articles:
  1. Fractals and fractal correlations. Computers in Physics, 8(4):420-425, 1994, with L.M. Sander and R.M. Ziff. Text and BW figures and Color figures.
  2. A new proof of the stable manifold theorem. Journal of Applied Mathematics and Physics (ZAMP), 47:497-513, 1996, with R. McGehee.
  3. Hyperbolic sets for noninvertible maps and relations. Discrete and Continuous Dynamical Systems, 5(2):339-358, 1999.
  4. Monte Carlo simulations for spinodal decomposition. Journal of Statistical Physics, 95(5-6):925-948, 1999, with T. Wanner.
  5. Homoclinic tangles for noninvertible maps. Nonlinear Analysis, 41(1-2):259-276, 2000.
  6. Unexpectedly linear behavior for the Cahn-Hilliard equation. SIAM Journal on Applied Mathematics, 60(6):2182-2202, 2000, with T. Wanner.
  7. Spinodal decomposition: A survey of recent results. In: B. Fiedler, K. Gröger, and J. Sprekels (editors), Equadiff 99, Proceedings of the International Conference on Differential Equations, 2:1288-1299, World Scientific, 2000, with S. Maier-Paape and T. Wanner.
  8. Limits to the Experimental Detection of Nonlinear Synchrony. Physical Review E, 65, 2002, 046225, with P. So, E. Barreto, K. Josic, and S.J. Schiff.
  9. Explosions: Global bifurcations at heteroclinic tangencies. Ergodic Theory and Dynamical Systems, 22(4):953-972, 2002, with K. Alligood and J. Yorke.
  10. The geometry of chaos synchronization. Chaos, 13(1):151-164, 2003, with E. Barreto, K. Josic, C. Morales, and P. So.
  11. Pattern Formation in a Nonlinear Model for Animal Coats. Journal of Differential Equations, 191(1):143-174, 2003, with T. Wanner.
  12. The Structure of Synchronization Sets for Noninvertible Systems . Chaos, 14(2):249-262, 2004, with K. Josic. Supplementary material.
  13. Dynamics of noninvertibility in delay equations. Discrete and Continuous Dynamical Systems Special Issue, 768-777, 2005, with E. Barreto, S. Schiff, and P. So.
  14. Complex transient patterns on the disk. Discrete and Continuous Dynamical Systems, Series A, 15(4):1049-1078, 2006, with J. P. Desi and T. Wanner.
  15. Three-dimensional crisis: Crossing bifurcations and unstable dimension variability. Phys. Rev. Lett. 96, 244103 (2006), with K.T. Alligood and J.A. Yorke.
  16. Explosions in dimensions one through three. Rendiconti del Seminario Matematico, Torino, 65(1): 1-15, 2007, with K.T. Alligood and J.A. Yorke.
  17. A classification of explosions in dimension one. Ergodic Theory and Dynamical Systems, 29: 715-731, 2009, with J.A. Yorke.
  18. Period-doubling cascades for large perturbations of Henon families. Journal of Fixed Point Theory and Applications, 6(1): 153-163, 2009, DOI: 10.1007/s11784-009-0116-7, with J.A. Yorke.
  19. Fixed points indices and period-doubling cascades. Journal of Fixed Point Theory and Applications, 8 (2010) 151-176, DOI 10.1007/s11784-010-0029-5, with M.R. Joglekar and J.A. Yorke.
  20. Period-doubling cascades galore. Ergodic Theory and Dynamics Systems, 31 (2011), 1249-1267, with J.A. Yorke.
  21. The dynamics of nucleation in stochastic Cahn-Morral systems. SIAM Journal on Applied Dynamical Systems (SIADS), 10(2): 707-743, 2011, DOI: 10.1137/100801378. with Jonathan P. Desi, Hanein Edrees, Joseph J. Price, and T. Wanner. This paper made the top 20 list of downloaded articles in June, July, August, September, October, and November, 2011.
  22. Connecting period-doubling cascades to chaos. International Journal of Bifurcation and Chaos, 22 (2), 2012, DOI: 10.1142/S0218127412500228, with J.A. Yorke. The article made the cover.
  23. Pattern formation in a mixed local and nonlocal reaction-diffusion system. Electronic Journal of Differential Equations, 2012(160): 1-30, 2012, with R. Tatum.
  24. Branch interactions and long-term dynamics for the diblock copolymer model in one dimension. Discrete and Continuous Dynamical Systems- Series A, 33(8): 3671 - 3705, 2013, with I. Johnson and T. Wanner.
  25. A Period-Doubling Cascade Precedes Chaos for Planar Maps. Chaos, 23(3): 033113, 2013. DOI: 10.1063/1.4813600, with J.A. Yorke.
  26. The many facets of chaos. International Journal of Bifurcation and Chaos, 25(4), 15300, 2015, DOI:10.1142/S0218127415300116. with J.A. Yorke. Featured article. Cover article.
  27. Chaos and its manifestations, SIAM News, 48(7), September 2015, with J. Yorke.
  28. Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites, Journal of Computational Neuroscience . 40(1): 27-50, 2015. DOI: 10.1007/s10827-015-0582-4, with R.I. Reznik, E. Barreto, and P. So.
  29. Quasiperiodicity: Rotation Numbers, Proceeding of The Foundations of Chaos Revisited: From Poincare to Recent Advancements, Chapter 7, 103-118, Springer Complexity, Switzerland, 2016, DOI: 10.1007/978-3-319-29701-9, with S. Das, Y. Saiki, and J. A. Yorke.
  30. Degenerate Nucleation in the Cahn-Hilliard-Cook Model, SIAM Journal on Applied Dynamical Systems (SIADS), 15(1): 459-494, 2016. DOI: 10.1137/15M1028844, with D. Blömker and T. Wanner.
  31. Measuring Quasiperiodicity, Europhysics Letters. 114 (2016) 40005, with S. Das, C.B. Dock, Y. Saiki, M. Salgado-Flores, E. Sander, J. Wu, and J. A. Yorke.
  32. Validated Bifurcation Methods and Applications to Lattice Dynamical Systems, SIAM Journal on Applied Dynamical Systems (SIADS), 15-3 (2016) 1690-1733, DOI: 10.1137/16M1061011, with T. Wanner.
  33. Generalized Lorenz Equations on a Three-Sphere, The European Physical Journal Special Topics 226 (9) 1751–1764, 2017. DOI:10.1140/epjst/e2017-70055-y, with Y. Saiki and J.A. Yorke.
  34. Quantitative Quasiperiodicity, to appear, Nonlinearity, with S. Das, Y. Saiki, and J.A. Yorke.

Other published works:
  1. Geometry Forum articles. Report GCG69, Geometry Center, University of Minnesota, 1994.
  2. Further Geometry Forum articles. Report GCG83, Geometry Center, University of Minnesota, 1995, with R. Hesse.
  3. Hyperbolic Sets for Noninvertible Maps and Relations. PhD Thesis, University of Minnesota, 1996.
  4. Review of Women Becoming Mathematicians by Margaret Murray, in American Scientist, January-February, 2001.
  5. A description of the DSWeb Tutorials Competition. Dynamical Systems Magazine, July, 2005.
  6. Critical Exponents, Cardiac Dynamics, and History in the DSWeb Tutorials Section . Dynamical Systems Magazine, October, 2005.
  7. DSWeb Tutorials Competition '07. Dynamical Systems Magazine, July, 2007.
  8. Noninvertibility, an entry in Scholarpedia, the free peer reviewed encyclopedia, 4(8):2242, 2009, with E. Barreto and P. So.
  9. Epidemics in the presence of social attraction and repulsion. Mathematical Modelling of Zombies, 2014, with C.M. Topaz.
  10. The Dynamical Systems Track at ICIAM 2011 in Vancouver. Dynamical Systems Magazine, October, 2011.
  11. GMU Math Makerbot Lab, a blog detailing mathematical 3D printing in the Math Department at George Mason, Started 2014.

Submitted papers:
  1. Finding the rotation number of any map from a quasiperiodic torus to a circle, submitted for publication, with S. Das, Y. Saiki, J.A. Yorke.
  2. Rigorous continuation of bifurcation points in the diblock copolymer equation, submitted for publication, with J-P Lessard and T. Wanner.


University of Minnesota: Georgia Institute of Technology: George Mason University:

Master's committee, Jennifer Attanasi, 2001.
Advisor, Robert Allen, undergraduate senior thesis, "Turing instabilities and spatial pattern formation in one dimension," August, 2003.
Master's project advisor, Karen Crossin, December, 2003.
Advisor, Tyler White, GMU-funded undergraduate research apprenticeship, $1100 Summer, 2005, renewed $1100 Fall, 2005. He was also a research assistant. Advisor for his honors senior thesis, "A neurological model for shell pattern formation," Spring, 2006.
Advisor, Hanein Edrees and John Price, 2007-08, "Phase separation dynamics in multi-component alloys," as part of the URCM program, joint with Thomas Wanner. They presented a poster of their results at the SIAM Annual Meeting in July, 2008.
Master's committee, Lihong Han, December, 2006.
Advisor, Anne Costolanski, Masters Thesis, "Explosion points in skew maps," July 24, 2007. She was awarded the department's outstanding graduate student award.
Research project with doctoral student Robert Allen (advisor Flavia Colonna).
Master's committee, Elan Rodan, August, 2008.
Advisor, "Nucleation and spinodal decomposition in ternary-component alloys" (and paper) undergraduate students Colleen Ackermann (Virginia Tech) and William Hardesty (UMBC), Summer, 2009, REU program, joint with Thomas Wanner.
Advisor, James O'Beirne, 2009-2010, URCM program, joint with Thomas Wanner.
Advisor, Richard Tatum, PhD, SCS, Analysis of a reaction-diffusion system with local and nonlocal diffusion terms, July 15, 2010.
Advisor, Olga Stulov (SUNY-New Palz), Stability of Equilibria in one dimension for Diblock Copolymer Equation Summer, 2010, REU program, joint with Thomas Wanner.
Advisor, Ian Johnson, "Numerical Continuation for a Diblock Copolymer Model in One Dimension," 2010-2011, URCM program, joint with Thomas Wanner.
Master's committee, Mike Atkins, May, 2011.
Master's project advisor, Vanessa Little, July, 2011.
Advisor, Kalea Sebesta, "Nucleation in a Two Component Metal Alloy," Summer 2013, REU program, joint with Thomas Stephens and Thomas Wanner.
Advisor, Nima Namazi, The Dynamics of Nucleation in Cahn-Hilliard-Cook Systems, 2013-14, URCM program, joint with Thomas Stephens and Thomas Wanner.
Advisor, Michael Crone, PhD, Math, Dynamics of harvested resources, with emphasis on commercially exploited fisheries, January 9 2015.
Advisor, James Trichilo, 2015-16, EXTREEMS Program, joint with Thomas Wanner.
Patrick O'Neal, 3D print lab, 2015-16.
Advisor, Robert Reznik, PhD, CSI, "Electric Field Effects On Single And Small Networks Of Neurons," January 20, 2016.
Advisor, Harout Boujakjian, Kathleen McLane, Conor Nelson, Spring 2016, MEGL Program.
Advisor, Arsah Rahman, Fall 2016, MEGL Program.
External PhD committee member, Yeyao Hu, GWU (student of Xiaofeng Ren), April 1, 2016.
External PhD committee member, Serap Tay-Stamoulas, UMBC (student of Muruhan Rathinam), June 17 2016.
Ratna Khatri, 3D print lab, 2016-17.
Advisor, Arsah Rahman, 2017, EXTREEMS Program.
Current doctoral students: Vandana Saini (Math), Sayomi Stallings (Math).
Patrick Bishop, Arsah Rahman, 3D print lab, 2017-18.

Sessions/Meetings organized:

Professional activities:

Editorial boards and professional positions

Referee and reviewing activities

2000-01, GMU math department transfer credit evaluation.
2001-2010, Graduate committee.
2003, Exploratory committee for a George Mason University Ph.D. in Mathematical Sciences.
2006-present, Preliminary Exam Committee: Algebra, Linear Analysis, Numerical Analysis, Ordinary Differential Equations.
2006-08, Policy and Hiring Committee.
2006, 2007, 2008, GMU Summer Research Proposal Review.
2007, Search Committee, Neuroscience/Biophysics Postdoc, Center for Neural Dynamics.
2007-2012, Organizer, Applied and Computational Math Seminar, with M. Emelianenko (until Fall 2010) and D. Anderson (starting Fall 2010).
2008-2010, In charge of scheduling of all math graduate courses.
2010-2011, elected adhoc member of the COS P&T Committee.
2011-2012, GMU Math Club Faculty Advisor.
2011-2012, Director of the Undergraduate Research in Computational Math (NSF-sponsored CSUMS) program.
2012, Hiring committee for postdocs, Institute for Mathematics and Its Applications, Minnesota.
Fall 2012-14, Department Policy and Hiring Committee.
2013, Performed teaching peer reviews (3 spring, 2 fall).
2013-14, Chair of hiring committee.
2014-15, Curator of the Mathematical Sciences art exhibit, Exploratory Hall display case.
2015-16 Performed teaching peer reviews (3 fall).
2017 (March 31) Academic panelist, Math department professional development event
2017 Performed teaching peer reviews (2 spring).
2017 Director of the EXTREEMS Undergraduate Research Program, with Dan Anderson.