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**Xiaoying (Maggie) Han
PhD, ASA**
Marguerite Scharnagle Endowed Professor in Mathematics
Department of Mathematics & Statistics
Auburn University
Auburn, Alabama
My main research interests are in random and nonautonomous dynamical systems and their applications. My current interests focus on modeling, analysis and simulation of stochastic/random differential equations in the applied sciences.
I am affiliated with the Actuarial Mathematics program at AU: I teach courses for actuarial exams and conduct research in actuarial science related areas. I attained the ASA designation (Associate of the Society of Actuaries) in 2012 and am pursuing the FSA (Fellow of the Society of Actuaries).
Office: 312 Parker Hall, Auburn University, Auburn, AL 36849
Phone: +1-334-844-5884 (O)
Email: xzh0003@auburn.edu
Research Interests
* Random and non-autonomous dynamical systems and applications
* Modeling, analysis, and simulation of dynamical systems in biology, ecology, chemical engineering, etc.
* Complex lattice models in the life sciences
Publications
* X. Han, P. E. Kloeden | Random Ordinary Differential Equations and Their Numerical Solutions | Springer Nature, Singapore | (2017)
* X. Han, P. E. Kloeden | Attractors under discretisation | BCAM SpringerBriefs, Springer-Verlag, Cham |(2017)
* H. Bessaih, M. J. Garrido-Atienza, X. Han, B. Schmalfuss | Stochastic lattice dynamical systems with fractional noise | SIAM J. Math. Anal. 49| 1495--1518 (2017)
* X. Han | Dynamical analysis of chemotherapy models with time-dependent infusion | Nonlinear Analysis - RWA 34 | 459--480 (2017)
* L. Wang, X. Han, Y. Cao, H. Najm | Computational singular perturbations for stochastic chemical reaction systems with stiffness | Journal of Computational Physics 335 | 404--425 (2017)
* F. Bao, Y. Cao, X. Han, J. Li | Efficient particle filtering for Korteweg-de Vries equations | Stochastic and Dynamics 17 | 175008 (2017)
* T. Caraballo, X. Han | Applied Nonautonomous and Random Dynamical Systems | BCAM SpringerBriefs, Springer-Verlag, Cham |(2016)
* Y. Asai, T. Caraballo, X. Han, P. E. Kloeden | A random model for immune response to virus in fluctuating environments | Advances in Dynamical Systems and Control, Springer-Verlag |211--225 (2016)
* X. Han, P. E. Kloeden | Nonautonomous lattice systems with swiching effects and delayed recovery | J. Diff. Eqs. 261 | 2986--3009 (2016)
* T. Caraballo, R. Colucci, X. Han | Semi-Kolmogorov models for predation with indirect effects in random environments | Disc. Cont. Dyn. Sys. - B 21 | 2120--2143 (2016)
* E. Jakobsons, X. Han, R. Wang | General convex order on risk aggregation | Scandinavian Actuarial Journal 8 | 713--740 (2016)
* T. Caraballo, R. Colucci, X. Han | Nonautonomous dynamics of a semi-Kolmogorov population model with periodic forcing | Nonlinear Analysis: RWA 31 | 661--680 (2016)
* T. Caraballo, X. Han, B. Schmalfuss, J. Valero | Random attractors for stochastic lattice dynamical systems with infinite multiplicative noise | Nonlinear Analysis: TMA 130 | 255--278 (2016)
* T. Caraballo, R. Colucci, X. Han |Predation with indirect effects in fluctuating enviroments |Nonlinear Dynamics 84| 115-126 (2016)
* X. Han, R. Wang | Estimating credit portfolio loss distribution by a cross-entropy method | J. of Appl. Math. Comput. | DOI: 10.1007/s12190-015-0941-3 (2015)
* T. Caraballo, X. Han | A survey on Navier-Stokes models with delays: existence, uniqueness and asymptotic behavior of solutions | Disc. Cont. Dyn. Sys. - S 8 | 1079 -- 1101 (2015)
* T. Caraballo, X. Han, P. E. Kloeden | Non-autonomous chemostats with variable delays |SIAM J. Math. Anal. 47 | 2178--2199 (2015)
* T. Caraballo, X. Han, P. E. Kloeden | Chemostats with random inputs and wall growth | Math. Meth. Appl. Sci. |DOI: 10.1002/mma.3437 (2015)
* X. Han, J. Li, D. Xiu | Error Analysis for the numerical formulation of particle filter |Disc. Cont. Dyn. Syst. - B 20 |1337--1354 (2015)
* T. H. Ahn, A. Sandu, X. Han | Advanced implicit tau-leaping methods for the stochastic simulation of chemical kinetics |J. Appl. Anal. Comput. 5 |420--452 (2015)
* T. Caraballo, X. Han, P. E. Kloeden, A. Rapaport | Dynamics of non-autonomous chemostat models |Continuous and Distributed Systems II (eds. V. A. Sadovnichiy, M. Z. Zgurovsky), Springer-Verlag | 103--120 (2015)
* X. Han | Asymptotic dynamics of stochastic lattice systems: a review |Continuous and Distributed Systems II (eds. V. A. Sadovnichiy, M. Z. Zgurovsky), Springer-Verlag|121--137 (2015)
* T. Caraballo, X. Han, P. E. Kloeden | Chemostats with time-dependent input and wall growth | Applied Mathematics and Information Sciences 9 | 2283--2296(2015)
* E. Jakobsons, X. Han, R. Wang | General convex order on risk aggregation | Scandinavian Actuarial Journal | DOI: 10.1080/03461238.2015.1007891 (2015)
* T. Caraballo, X. Han | Stability of stationary solutions to 2D-Navier-Stokes models with delays | Dynamics of Partial Differential Equations 11 |345--359 (2014)
* X. Han, H. Njam | Dynamical structures in stochastic chemical reaction systems | SIAM Journal on Applied Dynamical Systems 13 | 1033--1351 (2014)
* F. Bao, Y. Cao, X. Han | An implicit algorithm of solving nonlinear filtering problems | Communications in Computational Physics 16 | 382--402 (2014)
* S. Zhou, X. Han | Uniform exponential attractors for non-autonomous KGS and Zakharov lattice systems with quasi-periodic external forces | Nonlinear Analysis Series A: Theory, Methods & Applications 78| 141--155 (2013)
* X. Han | Asymptotic behaviors for second order stochastic lattice dynamical systems on Z^k in weighted spaces | Journal of Mathematical Analysis and Applications 2013 | 242--254 (2013)
* S. Zhou, X. Han | Pullback exponential attractors for non-autonomous lattice systems | Journal of Dynamics and Differential Equations 24 | 601--631 (2012)
* X. Han | Random attractors for second order stochastic lattice dynamical systems with multiplicative noise in weighted spaces | Stochastic and Dynamics 12 | 1150024 (2012)
* X. Han | Asymptotic behavior for stochastic partly dissipative lattice systems in weighted spaces | International Journal of Differential Equations 2011 | 628459 (2011)
* X. Han | Exponential attractors for lattice dynamical systems in weighted spaces | Discrete and Continuous Dynamical Systems - series A 31 | 445--467 (2011)
* X. Han | Random attractors for stochastic sine-Gordon lattice systems with multiplicative white noise | Journal of Mathematical Analysis and Applications 376 | 481--493 (2011)
* X. Han, W. Shen, S. Zhou | Random attractors for stochastic lattice dynamical systems in weighted spaces | Journal of Differential Equations 250 | 1235--1266 (2010)
* Z. Shen, S. Zhou, X. Han | Synchronization of coupled stochastic systems with multiplicative noise | Stochastic and Dynamics 10 | 407--428 (2010)
* X. Han, B. Spencer | Composition evolution of quantum dots during the growth of solid films | IMA Journal of Applied Mathematics 75 | 222--239 (2010)
* S. Zhou, J. Huang, X. Han | Compact kernel sections for dissipative non-autonomous Zakharov equation on infinite lattices | Communications on Pure and Applied Analysis 9 | 193--210 (2009)
* J. Huang, X. Han, S. Zhou | Uniform attractors for dissipative non-autonomous Klein-Gordon-Schrodinger lattice systems | Applied Mathematics and Mechanics 30 | 1579--1607 (2009)
* A. Ban, S. Zhou, X. Han | Dimension of kernel sections for damped nonautonomous wave equations with critical exponent | Journal of Mathematical Physics 50 | 012702 (2009)
* X. Han, B. Spencer | A Nonlinear model for surface segregation and solute trapping during planar film growth | Journal of Applied Physics 101 | 084302 (2007)
Invited Presentations
* "Stochastic computational singular perturbation for stiff chemical Langevin equations", Colloquium, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China (2017)
* "Dynamical structures in stochastic chemical reaction systems", Mathematical Congress of the Americas, Montreal, Canada (2017)
* "Computational singular perturbation analysis of stochastic chemical reaction systems", The 6th International Workshop on Model Reduction in Reacting Flows, Princeton, NJ (2017)
* "Attractors for nonautonomous lattice systems with switching effects and delayed recovery", Workshop on Pullback Attractors: Deterministic and Random, Wuhan, China (2017)
* "Nonautonomous lattice systems with switching effects and delayed recovery", ICMC Summer Meeting on Differential Equations, Sao Carlos, Brazil (2017)
* "Dynamical analysis of ecological systems in varying environments", Applied Math Colloquium, Program in Applied Mathematics, University of Arizona, Tucson, AL (2016)
* "Numerical dynamics of random ordinary differential equations", The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL (2016)
* "Semi-Kolmogorov's predator-prey models in varying environments", The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, FL (2016)
* "Predation models with indirect effects under fluctuating enviroments", The 10th International Conference on Recent Advances in Applied Dynamical Systems, Xuzhou, China (2016)
* "Dynamic model reduction for stochastic chemical reaction systems with stiffness", SIAM Conference on Uncertainty Quantification, Lausanne, Switzerland (2016)
* "Semi-Kolmogorov type of predation models in varying environments", Colloquium, School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China (2016)
* "Asymptotic dynamics for stochastic lattice systems with infinite multiplicative white noise", Workshop in Stochastic Dynamics, Beijing, China (2015)
* "Random attractors for stochastic lattice dynamical systems", EquaDiff, Lyon, France (2015)
* "Construction of random low-dimensional manifolds for stochastic chemical systems", The 5th International Workshop on Model Reduction in Reacting Flows, Cottbus, Germany (2015)
* "Chemostat in varying environments", 7th International Conference on Dynamic Systems and Applications, Atlanta, GA (2015)
* " An implicit scheme for nonlinear filtering problems", 45th Annual John H. Barrett Memorial Lectures, University of Tennessee, TN (2015)
* "An introduction to biological/biochemical systems", Colloquium, Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, China (2015)
* "Dynamics of stochastic fast-slow chemical reaction networks", ICMC Summer Meeting on Differential Equations, Sao Carlos, Brazil (2015)
* "Long term behavior of stochastic lattice dynamical systems in the weighted spaces", Seminar, Friedrich-Schiller-Universitat Jena, Jena, Germany (2014)
* "Nonautonomous and random chemostat models", Seminar, Department of Mathematics, Wayne State University, Detroit, MI (2014)
* "Dynamics of stochastic chemical reaction systems", Conference on Dynamical Systems and Applications, Wuhan, China (2014)
* "Chemostats with time-dependent inputs and wall growth", The 10th AIMS Conference on Dynamical Systems and Differential Equations, Madrid, Spain (2014)
* "Implicit simulation Methods for Stochastic chemical kinetics", The 10th AIMS Conference on Dynamical Systems and Differential Equations, Madrid, Spain (2014)
* "Fundamentals of financial mathematics", Mini-course, Instituto Mathematicas Universidad Sevilla, Seville, Spain (2014)
* "Analysis of chemostat models with non-autonomous and random inputs", Seminar Series, Facultad de Mathematicas, Universidad Sevilla, Seville, Spain (2014)
* "Numerical and implicit schemes for nonlinear stochastic filtering problems", Seminar, Sandia National Laboratories, Livermore, CA (2014)
* "Nonlinear filtering and its applications", Colloquium, Department of Mathematical Science, Worcester Polytechnic Institute, Worcester, MA (2014)
* "An introduction to mathematics of financial derivatives", Seminar, Department of Mathematical Science, Worcester Polytechnic Institute, Worcester, MA (2014)
* "Numerical formulation of particle filtering for nonlinear stochastic systems", International Workshop on Infinite Dimensional Stochastic Systems, Wittenberg, Germany (2014)
* "Nonautonomous and stochastic differential equations and applications", East Lake Forum at Huazhong University of Science and Technology, Wuhan, China (2013)
* "An implicit nonlinear filtering algorithm", The 4th Wuhan Workshop on Stochastic Dynamics, Wuhan, China (2013)
* "Convergence results on methods for solving nonlinear filtering problems", The Second Pacific Rim Mathematical Association Congress, Shanghai, China (2013)
* "Dynamical structures in stochastic chemical reaction systems", The 4th International Workshop on Model Reduction in Reacting Flows, San Francisco, CA (2013)
* "Random attractors for stochastic lattice differential equations", One-day Workshop on Stochastic Differential Equations, Seville, Spain (2013)
* "Convergence results on methods for solving nonlinear filtering problems", Dynamical System Seminar, Institute of Mathematics and Its Applications, Minneapolis, MN (2013)
* "Dynamics of infinite dimensional stochastic differential equations", Colloquium, Department of Mathematics and Department of Statistics and Probability, Michigan State University, East Lansing, MI (2013)
* "Asymptotic behavior for stochastic lattice differential equations in weighted spaces", IMA Workshop: Lattice and Nonlocal Dynamical Systems and Applications, Minneapolis, MN (2012)
* "Asymptotic behavior for stochastic lattice differential equations in weighted spaces", SIAM Conference on Uncertainty Quantification, Raleigh, NC (2012)
* "Random attractors for stochastic lattice differential equations in weighted spaces", AMS 2012 Spring Southeaster Section Meeting, Tampa, FL (2012)
* "Asymptotic behavior of stochastic lattice differential equations", Colloquium, Statistical and Applied Mathematical Science Institute, Research Triangle Park, NC (2012)
* "An introduction to stochastic differential equations", Statistical and Applied Mathematical Sciences Institute Undergraduate Workshop, Research Triangle Park, NC (2011)
* "Surface segregation and solute trapping during the growth of thin films", Seminar, Department of Mathematics, North Carolina State University, Raleigh, NC (2011)
* "Random attractors for stochastic lattice dynamical systems", Seminar, School of Mathematical Sciences, Fudan University, Shanghai, China (2011)
* "Interlayer mixing in thin film growth", Mini-workshop on Dynamical Systems and Applications, Shanghai Jiaotong University, Shanghai, China (2011)
* "Random attractors for stochastic lattice differential equations", The 5th International Conference on Recent Advances in Applied Dynamical Systems, Shanghai, China (2011)
* "Random attractors for first order stochastic lattice dynamical systems", Seminar, Department of Mathematics, Shanghai Normal University, Shanghai, China (2010)
* "Composition evolution of quantum dots during the growth of solid films", IFNA-World Congresses of Nonlinear Analysis, Orlando, FL (2008)
* "Composition evolution of quantum dots during the growth of solid films", Mini-Workshop on Differential Equations and Applications, Auburn, AL (2008)
* "Interlayer mixing during thin film growth", Seminar, Department of Material Engineering, Auburn University, AL (2007)
* "Interlayer mixing during thin film growth", Seminar, Department of Mathematics, The State University of New York at Buffalo, Buffalo, NY (2007)
2019 | Fall |TBD | Spring | On Sabbatical leave
2018 | Fall | Linear Differential Equations (MATH2650-115) | Spring | Linear Differential Equations (MATH 2650) | Mathematics of Interest Theory (MATH 2790)
2017 | Fall | No Teaching | Spring | No Teaching
2016 | Fall | Financial Mathematics (MATH5870/6870) | Calculus with Business Applications (MATH1680) |Spring |No Teaching
2015 | Fall | Applied Mathematics (MATH 7000) | Financial Mathematics (MATH 5870/6870) |Spring | No Teaching
2014 | Fall | Actuarial Seminar in Mathematics of Finance (MATH 4790) | Mathematics Modeling: Continuous (MATH 5000/6000) | Spring | No Teaching
2013 | Fall | Actuarial Mathematics I (MATH5800/6800) | Linear Differential Equations (MATH2650) | Spring | No Teaching
2012 | Fall | Financial Mathematics (MATH5870/6870) | Spring | No Teaching
2011 | Fall | No Teaching | Spring | Linear Differential Equations (MATH 2650) | Mathematics of Interest Theory (MATH 2790)
2010 | Fall | No Teaching | Spring | Actuarial Mathematics II (MATH 5810/6810) | Analysis II (MATH 5210/6210)
2009 | Fall | Actuarial Mathematics I (MATH 5800/6800) | Analysis I (MATH 5200/6200) | Spring | Mathematics of Interest Theory (MATH 2790)
2008 | Fall | Actuarial Seminar in Mathematics of Finance (MATH 4790) | Mathematics Modeling: Continuous (MATH 5000/6000) | Spring | Mathematics of Interest Theory (MATH 2790)
2007 | Fall | Calculus II (MATH 1620) | Linear Differential Equations (MATH 2650)
Education
Ph.D. | Department of Mathematics, State University of New York at Buffalo
MA | Department of Mathematics, State University of New York at Buffalo
BE | The Special Class for the Gifted Young, University of Science and Technology of China
Professional Experience
Oct 2017 - Present | Professor of Mathematics, Auburn University, Auburn, AL
Oct 2012 - Sep 2017 | Associate Professor of Mathematics, Auburn University, Auburn, AL
Aug 2007 - Sep 2012 | Assistant Professor of Mathematics, Auburn University, Auburn, AL
May 2014 - Aug 2014 | Visiting Associate Professor at University of Waterloo, Canada
Jan 2013 - May 2013 | Visiting Scholar at IMA, Minneapolis, MN
Aug 2011 - Jun 2012 | Visiting Research Fellow at SAMSI, Raleigh, NC
Honors and Awards
* Marguerite Scharnagle Endowed Professor (2018--2020)
* Provost-funded Professional Improvement Leave (Spring 2019)
* Simon's Collaboration Grants for Mathematicians (2016--2021)
* Jack B. Brown Endowed Faculty Award (2015)
* AWM-NSF Travel Award (2014)
* NSF Travel Award (2013)
* Educational Institution ASA Grant (2012)
* COSAM Travel Award, Auburn University (2014, 2012)
* Butz Teaching Award, Auburn University (2011)
* Northrop Grumman Research Award (2009)
* Fellowship of College of Arts and Sciences at SUNY-Buffalo (2002--2006)

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