Robert Sacker

Tenure Track Appointments

• Professor, University of Southern California, 01/01/1977 –
• Associate Professor, University of Southern California, 01/01/1973 – 01/01/1977
• Visiting Associate Professor, University of Minnesota, 01/01/1972 – 01/01/1973
• Associate Professor, University of Southern California, 01/01/1969 – 01/01/1972
• Assistant Professor, University of Southern California, 01/01/1966 – 01/01/1969
• Visiting Member, Courant Institute of Mathematical Sciences, New York University, 01/01/1964 – 01/01/1969
• Adjunct Assistant Professor, Washington Square College, New York University, 01/01/1964 – 01/01/1966

Summary Statement of Research Interests

Professor Sacker’s reserach interests include: ordinary differential equations, difference equations, infinite dimensional dynamical systems, applied mathematics, mathematical biology including modelling e-coli evolution in a test tube..

Research Specialties

Dynamical Systems, Mathematical Biology

Conference Presentations

• Global Stability of the Fixed Point of Certain Planar Maps , IMA(Institute of Mathematics and Applications)Talk/Oral Presentation, IMA, Invited, U. of Minnesota, Minneapolis, 2016-2017
• Phase as determined by Correlation is not sufficient for Resonance versus Attenuation in the Beverton-Holt model , International Conference on Difference Equations and ApplicationsTalk/Oral Presentation, Local Organizer, Invited, Barcelona, Spain, 2012-2013
• Some New Results in Periodic Difference Equations with Allee Effect: The Undereappreciated Role of Semigroups , 3rd International Conference On Math Modeling & AnalysisTalk/Oral Presentation, Invited, San Antonio, Texas, 2011-2012
• An Invariance Theorem for Mappings , AMS Special Session on Continuous and Discrete Dynamical SystemsTalk/Oral Presentation, American Mathematical Society, Invited, UCLA, 2010-2011
• On a Migration-Selection Model , Combined AMS, MAA, SIAM annual meetingTalk/Oral Presentation, American Mathematical Society, SIAM, MAA, Invited, New Orleans, Louisiana, 2010-2011
• Global stability in a multi-species periodic Leslie-Gower model , The 2nd Internat. Conf. on Mathematical Modeling and Analysis of Populations in Biological SystemsTalk/Oral Presentation, Organizer, Invited, Huntsville, Alabama, 2009-2010
• Dynamic Reduction, the Periodic Ricker map and Genetically Altered Mosquitos , Conference on Progress in Difference EquationsTalk/Oral Presentation, Organizer, Invited, Laufen, Bavaria, Germany, 2006-2007
• Population Models with Allee effect , 12th International Conference on Difference Equations and ApplicationsTalk/Oral Presentation, Organizer, Invited, Lisbon, Portugal, 2006-2007
• The periodically forced Giesl, Meisel, Scheurle, Wagner model, or “Drinking Beer in a Rocking Chair” , Workshop on Mathematical Stability Analysis in Biomechanics and RoboticsTalk/Oral Presentation, Organizer, Invited, Bielefeld, Germany, 2006-2007
• Dynamic Reduction and the Modified Ricker map:\ From Genetically Altered Mosquitos to E-coli Growth and Mutation , 11th International Conference on Difference Equations and ApplicationsTalk/Oral Presentation, Organizer, Invited, Kyoto, 2005-2006
• The Stochastic Beverton-Holt Equation , 10th International Conference on Difference Equations and ApplicationsTalk/Oral Presentation, International Society of Difference Equations , Invited, Munich, Germany, 2004-2005

Other Presentations

• Global stability in a multi-species periodic Leslie-Gower model, Colloquium, Lafayette, Louisiana, 2010-2011
• Semigroups of Maps and Periodic Difference Equation, AMS Special Session on Discrete Dynamical Systems in Periodic Environments, Washington DC, 2008-2009
• Dynamic Reduction with Applications to Discrete Systems, Sectional Meeting, Claremont McKenna, 2007-2008
• Dynamic Reduction, the Periodic Ricker map and Genetically Altered Mosquitos, Colloquium, Houston, Texas, 2007-2008
• Population Models with Allee effect , Colloquium, San Antonio, TX, 2007-2008
• Population Models with Allee effect , Conference on Biology and Dynamics, Tucson, AZ, 2007-2008
• Semigroups of Maps and Periodic Difference Equations, Colloquium, Claremont, CA, 2007-2008
• Dynamic Reduction and the Modified Ricker map:\ From Genetically Altered Mosquitos to E-coli Growth and Mutation, Seminar, Los Angeles, CA, 2006-2007
• Dynamic Reduction with applications to Mathematical Biology and other areas, Colloquium,, Texas, 2006-2007
• The Stochastic Beverton-Holt Equation, Colloquium,, Minneapolis, MN, 2004-2005
• The Stochastic Beverton-Holt Equation , Colloquium, San Antonio, TX, 2004-2005

Book Review

• Pötzsche, C. (2014). Geometric Theory of Discrete Nonautonomous Dynamical Systems. Springer. pp. 506-510.

Journal Article

• Sacker, R. J. (2021). A New Metric Yielding a Richer Class of Unbounded Functions Having Compact Hulls in the Shift Flow. Journal of Dynamics and Differential Equations.
• Sacker, R. J. (2019). Bifurcation in the Almost Periodic Ricker Map. J. of Difference Eq./Taylor & Francis. Vol. doi.org/10.1080/10236198.2019.1604696
• Haskell, C., Sacker, R. J. (2019). Attenuation in the Almost Periodic Beverton-Holt Equation. L. Difference Eq./ Taylor & Francis. Vol. 25 (4), pp. 542-547.
• Ryals, B., Sacker, R. J. (2018). Global Stability in the 2D Ricker Equation Revisited. Discrete and Continuous Dynamical Systems, B.
• Sacker, R. J., Sell (Deceased), G. R. (2017). Almost Periodicity, Ricker Map, Beverton-Holt Map and Others, a General Method. Journal of Difference Equations and Applications/Taylor & Francis. Vol. 22 (7), pp. 1286-1297.
• Sacker, R. J., Sell, G. R. (2017). Almost Periodicity, Ricker Map, Beverton-Holt Map and Others, a General Method. J. Difference Eq. and Applications, Taylor & Francis. Vol. 23 (7), pp. 1286-1297.
• Sacker, R. J. (2017). Almost Periodicity, Ricker Map, Beverton-Holt Map\ and Others, a General Method. Journal of Difference Equations and Applications, Taylor & Francis. pp. 12.
• Ryals, B., Sacker, R. J. (2015). Global stability in the 2D Ricker equation. Journal of Difference Equations and Applications/Taylor and Francis. Vol. 21 (11), pp. 1068-1081. On line link to paper
• Ackleh, A. S., Sacker, R. J., Salceanu, P. (2014). On a Discrete Selection-Mutation Model. Journal of Difference Equations and Applications/Taylor & Francis. Vol. DOI, pp. 18. http://www.tandfonline.com/doi/full/10.1080/10236198.2014.933819#tabModule
• Yang, Y., Sacker, R. J. (2014). Periodic Unimodal Allee Maps, the Semigroup Property and the Lambda-Ricker Map with Allee Effect. Discrete and Continuous Dynamical Systems-B/American Institute of Mathematical Sciences. Vol. 19 (2), pp. 589-606. http://AIMSciences.org
• Yang, Y., Sacker, R. J. (2013). Resonance and Attenuation in the n-periodic Beverton-Holt Equation. Journal of Difference Equations and Applications/Taylor and Francis. Vol. 19 (8-9), pp. 1174-1191.
• Sacker, R. J. (2012). A Note: An Invariance Theorem for Mappings II. Journal of Dynamics and Differential Equations/Springer. Vol. 24 (3), pp. 595-599.
• Gaut, G. R., Goldring, K., Grogan, F., Haskell, C., Sacker, R. J. (2012). Diference Equations with Allee Effect and The Periodic Sigmoid Beverton-Holt Equation Revisited. Journal of Biological Dynamics/Taylor & Francis. Vol. 6 (2), pp. 1019-1033.
• Sacker, R. J. (2011). Global stability in a multi-species periodic Leslie-Gower model. Journal of Biological Dynamics/ Taylor & Francis. Journal of Biological Dynamics
• Sacker, R. J. (2010). A note: an invariance theorem for mappings. Journal of Difference Equations and Applications.
• Sacker, R. J., Von Bremen, H. F. (2010). A Conjecture on the Stability of the Periodic Solutions of Ricker’s Equation With Periodic Parameters.
• Sacker, R. J., Elaydi, S. (2010). Population Models with Allee effect: A New Model. Journal of Biological Dynamics/ Taylor & Francis. Vol. 4 (4), pp. 397-408.
• Sacker, R. J. (2010). Semigroups of Maps and Periodic Difference Equations. Journal of Difference Equations and Applications.
• Sacker, R. J. (2009). Introduction to the 2008 Re-Publication of the “Neimark-Sacker Bifurcation Theorem. Journal of Difference Equations and Applications. pp. 6.
• Sacker, R. J., Von Bremen, H. F. (2007). Dynamic Reduction with applications to Mathematical Biology and other areas. Journal of Biological Dynamics / Taylor & Francis. Vol. 1 (4), pp. 1-17.
• Sacker, R. J. (2007). A Note on Periodic Ricker Maps. Journal of Difference Equations and Applications/Taylor and Francis. Vol. 13 (1), pp. 89-92.
• Elaydi, S., Sacker, R. J. (2006). Periodic difference equations, population biology and the Cushing-Henson conjectures. Mathematical Biosciences/Elsevier. Vol. V. 201, pp. 195-207.
• Haskell, C., Sacker, R. J. (2005). The Stochastic Beverton-Holt Equation and the M. Neubert Conjecture. Journal of Dynamics and Differential Equations/Elsevier. Vol. V. 17 (No. 4), pp. pp. 825-842.
• Elaydi, S., Sacker, R. J. (2005). Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures. Journal of Difference Equations and Applications/Taylor & Francis. Vol. Vol. 11 (4 & 5), pp. p. 337-346.
• Elaydi, S., Sacker, R. J. (2005). Global stability of periodic orbits of nonautonomous difference equations and population biology. Journal of Differential Equations/Elsevier. Vol. 208 (1), pp. p. 258 – 273.
• Elaydi, S., Sacker, R. J. (2004). Basin of attraction of periodic orbits of maps on the real line. Journal of Difference Equations and Applications/Taylor & Francis. Vol. Vol. 10 (10), pp. p. 881-888.
• Sacker, R. J., Von Bremen, H. F. (2003). “A new approach to cycling in a 2-locus 2-allele genetic model”. J. Difference Equations and Applications, Taylor & Francis. Vol. 9 (5), pp. 441-448.
• Sacker, R. J., Bodine, S. (2001). Asymptotic diagonalization of linear difference equations, with Sigrun Bodine. Journal of Difference Equations and Applications. Vol. 7, pp. 637-650.
• Sacker, R. J., Bodine, S. (2000). A new approach to asymptotic diagonalization of linear differential systyems,. J. Dynamics and Differential Equations, Elsevier. Vol. 12 (1), pp. 229-245.

Proceedings

• Elaydi, S., Sacker, R. J. (2005). Skew-product dynamical systems: Applications to difference equations. Proceedings of the Second Annual Celebration of Mathematics, United Arab Emirates/Taylor & Francis.
• Sacker, R. J., von Bremen, H. F. (2005). Global asymptotic stability in the Jia Li model for genetically altered mosquitos. pp. p. 87-100. Difference Equations and Discrete Dynamical Systems/Taylor & Francis.
• Sacker, R. J., von Bremen, H. F. (2005). Some Stability Results in a Model for Genetically Altered Mosquitoes. pp. p. 301+308. Shaker Verlag.
• Elaydi, S., Sacker, R. J. (2005). Global stability of periodic orbits of nonautonomous difference equations in population biology and the Cushing-Henson conjectures. pp. p.113-126. Proceedings of 8th International Conference on Difference Equations and Applications Brno, Czech Republic/Chapman and Hall.

Other

• Sacker, R. J.Dichotomies for Linear Evolutionary Equations in Banach Space, Joint with G.

  Sell, J. Differential Eq. 113 pp. 17-67, 1994.

• Sholarpedia Web Page/ http://www.scholarpedia.org/, Describes the Neimark-Sacker bifurcation

  Authors:
  Yuri A. Kuznetsov and
  Robert J. Sacker
  URL: http://www.scholarpedia.org/article/Neimark-Sacker_bifurcation, 2007-2008

• Nominated for the Bernd Aulbach Prize for significant contributions to the areas of difference equations and/or discrete dynamical systems, 2012-2013
• Special Journal issue dedicated to R J Sacker, 2009-2010

Editorships and Editorial Boards

• Co-Editor, Journal of Difference Equations and Applications — Short Notes Section, 2003 –

Professional Memberships

• Chairman: Organizing committee, 9th International Conference on Difference Equations and Applications, http://math.usc.edu/~rsacker/icdea2004, 2003