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Robert Sacker

Professor of Mathematics

Contact Information
E-mail: rsacker@usc.edu
Phone: (213) 740-3793
Office: KAP 438A

LINKS
Faculty Profile on Departmental Website
Personal Website
Course Information
 

Biographical Sketch

Link
 

Education

Ph.D. Mathematics, New York University, Courant Institute, 1/1964
M.S. Mathematics, Georgia Institute of Technology, 1/1961
B.S. Mathematics, Georgia Institute of Technology, 1/1959
 

Academic Appointment, Affiliation, and Employment History

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  
 

Description of Research

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
 

Affiliations with Research Centers, Labs, and Other Institutions

USC Center for Applied Mathematical Sciences, http://www.usc.edu/dept/LAS/CAMS/
 

Conferences and Other Presentations

Conference Presentations

"Phase as determined by Correlation is not sufficient for Resonance versus Attenuation in the Beverton-Holt model", International Conference on Difference Equations and Applications, Talk/Oral Presentation, Barcelona, Spain, Local Organizer, Invited, 2012-2013   
"Some New Results in Periodic Difference Equations with Allee Effect: The Undereappreciated Role of Semigroups", 3rd International Conference On Math Modeling & Analysis, Talk/Oral Presentation, San Antonio, Texas, Invited, 2011-2012   
"An Invariance Theorem for Mappings", AMS Special Session on Continuous and Discrete Dynamical Systems, Talk/Oral Presentation, UCLA, American Mathematical Society, Invited, 2010-2011   
"On a Migration-Selection Model", Combined AMS, MAA, SIAM annual meeting, Talk/Oral Presentation, New Orleans, Louisiana, American Mathematical Society, SIAM, MAA, Invited, 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 Systems, Talk/Oral Presentation, Huntsville, Alabama, Organizer, Invited, 2009-2010   
"Dynamic Reduction, the Periodic Ricker map and Genetically Altered Mosquitos", Conference on Progress in Difference Equations, Talk/Oral Presentation, Refereed Laufen, Bavaria, Germany, Organizer, Invited, 2006-2007   
"Population Models with Allee effect", 12th International Conference on Difference Equations and Applications, Talk/Oral Presentation, Refereed Lisbon, Portugal, Organizer, Invited, 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 Robotics, Talk/Oral Presentation, Bielefeld, Germany, Organizer, Invited, 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 Applications, Talk/Oral Presentation, Kyoto, Organizer, Invited, 2005-2006   
"The Stochastic Beverton-Holt Equation", 10th International Conference on Difference Equations and Applications, Talk/Oral Presentation, Munich, Germany, International Society of Difference Equations , Invited, 2004-2005   
 

Other Presentations

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

Publications

Book Review

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

Journal Article

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.
 

Other

Sacker, R. J. Dichotomies for Linear Evolutionary Equations in Banach Space, Joint with G. Sell, J. Differential Eq. 113 pp. 17-67, 1994.
 

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.
 

Multimedia Scholarship and Creative Works

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   
 

Honors and Awards

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   
 

Service to the Profession

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  
Society of Mathematical Biology, 2002  
 
 
Faculty may update their profile by visiting https://mydornsife.usc.edu.