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. KloedenRandom Ordinary Differential Equations and Their Numerical SolutionsSpringer Nature, Singapore(2017)
  • X. Han, P. E. KloedenAttractors under discretisationBCAM SpringerBriefs, Springer-Verlag, Cham(2017)
  • H. Bessaih, M. J. Garrido-Atienza, X. Han, B. SchmalfussStochastic lattice dynamical systems with fractional noiseSIAM J. Math. Anal. 491495--1518 (2017)
  • X. HanDynamical analysis of chemotherapy models with time-dependent infusionNonlinear Analysis - RWA 34459--480 (2017)
  • L. Wang, X. Han, Y. Cao, H. NajmComputational singular perturbations for stochastic chemical reaction systems with stiffnessJournal of Computational Physics 335404--425 (2017)
  • F. Bao, Y. Cao, X. Han, J. LiEfficient particle filtering for Korteweg-de Vries equationsStochastic and Dynamics 17175008 (2017)
  • T. Caraballo, X. HanApplied Nonautonomous and Random Dynamical SystemsBCAM SpringerBriefs, Springer-Verlag, Cham(2016)
  • Y. Asai, T. Caraballo, X. Han, P. E. KloedenA random model for immune response to virus in fluctuating environmentsAdvances in Dynamical Systems and Control, Springer-Verlag211--225 (2016)
  • X. Han, P. E. KloedenNonautonomous lattice systems with swiching effects and delayed recoveryJ. Diff. Eqs. 2612986--3009 (2016)
  • T. Caraballo, R. Colucci, X. HanSemi-Kolmogorov models for predation with indirect effects in random environmentsDisc. Cont. Dyn. Sys. - B 212120--2143 (2016)
  • E. Jakobsons, X. Han, R. WangGeneral convex order on risk aggregationScandinavian Actuarial Journal 8713--740 (2016)
  • T. Caraballo, R. Colucci, X. HanNonautonomous dynamics of a semi-Kolmogorov population model with periodic forcingNonlinear Analysis: RWA 31661--680 (2016)
  • T. Caraballo, X. Han, B. Schmalfuss, J. ValeroRandom attractors for stochastic lattice dynamical systems with infinite multiplicative noiseNonlinear Analysis: TMA 130255--278 (2016)
  • T. Caraballo, R. Colucci, X. HanPredation with indirect effects in fluctuating enviromentsNonlinear Dynamics 84115-126 (2016)
  • X. Han, R. WangEstimating credit portfolio loss distribution by a cross-entropy methodJ. of Appl. Math. Comput.DOI: 10.1007/s12190-015-0941-3 (2015)
  • T. Caraballo, X. HanA survey on Navier-Stokes models with delays: existence, uniqueness and asymptotic behavior of solutionsDisc. Cont. Dyn. Sys. - S 81079 -- 1101 (2015)
  • T. Caraballo, X. Han, P. E. KloedenNon-autonomous chemostats with variable delaysSIAM J. Math. Anal. 472178--2199 (2015)
  • T. Caraballo, X. Han, P. E. KloedenChemostats with random inputs and wall growthMath. Meth. Appl. Sci.DOI: 10.1002/mma.3437 (2015)
  • X. Han, J. Li, D. XiuError Analysis for the numerical formulation of particle filterDisc. Cont. Dyn. Syst. - B 201337--1354 (2015)
  • T. H. Ahn, A. Sandu, X. HanAdvanced implicit tau-leaping methods for the stochastic simulation of chemical kineticsJ. Appl. Anal. Comput. 5420--452 (2015)
  • T. Caraballo, X. Han, P. E. Kloeden, A. RapaportDynamics of non-autonomous chemostat modelsContinuous and Distributed Systems II (eds. V. A. Sadovnichiy, M. Z. Zgurovsky), Springer-Verlag103--120 (2015)
  • X. HanAsymptotic dynamics of stochastic lattice systems: a reviewContinuous and Distributed Systems II (eds. V. A. Sadovnichiy, M. Z. Zgurovsky), Springer-Verlag121--137 (2015)
  • T. Caraballo, X. Han, P. E. KloedenChemostats with time-dependent input and wall growthApplied Mathematics and Information Sciences 92283--2296(2015)
  • E. Jakobsons, X. Han, R. WangGeneral convex order on risk aggregationScandinavian Actuarial JournalDOI: 10.1080/03461238.2015.1007891 (2015)
  • T. Caraballo, X. HanStability of stationary solutions to 2D-Navier-Stokes models with delaysDynamics of Partial Differential Equations 11345--359 (2014)
  • X. Han, H. NjamDynamical structures in stochastic chemical reaction systemsSIAM Journal on Applied Dynamical Systems 131033--1351 (2014)
  • F. Bao, Y. Cao, X. HanAn implicit algorithm of solving nonlinear filtering problemsCommunications in Computational Physics 16382--402 (2014)
  • S. Zhou, X. HanUniform exponential attractors for non-autonomous KGS and Zakharov lattice systems with quasi-periodic external forcesNonlinear Analysis Series A: Theory, Methods & Applications 78141--155 (2013)
  • X. HanAsymptotic behaviors for second order stochastic lattice dynamical systems on Z^k in weighted spacesJournal of Mathematical Analysis and Applications 2013242--254 (2013)
  • S. Zhou, X. HanPullback exponential attractors for non-autonomous lattice systemsJournal of Dynamics and Differential Equations 24601--631 (2012)
  • X. HanRandom attractors for second order stochastic lattice dynamical systems with multiplicative noise in weighted spacesStochastic and Dynamics 121150024 (2012)
  • X. HanAsymptotic behavior for stochastic partly dissipative lattice systems in weighted spacesInternational Journal of Differential Equations 2011628459 (2011)
  • X. HanExponential attractors for lattice dynamical systems in weighted spacesDiscrete and Continuous Dynamical Systems - series A 31445--467 (2011)
  • X. HanRandom attractors for stochastic sine-Gordon lattice systems with multiplicative white noiseJournal of Mathematical Analysis and Applications 376481--493 (2011)
  • X. Han, W. Shen, S. ZhouRandom attractors for stochastic lattice dynamical systems in weighted spacesJournal of Differential Equations 2501235--1266 (2010)
  • Z. Shen, S. Zhou, X. HanSynchronization of coupled stochastic systems with multiplicative noiseStochastic and Dynamics 10407--428 (2010)
  • X. Han, B. SpencerComposition evolution of quantum dots during the growth of solid filmsIMA Journal of Applied Mathematics 75222--239 (2010)
  • S. Zhou, J. Huang, X. HanCompact kernel sections for dissipative non-autonomous Zakharov equation on infinite latticesCommunications on Pure and Applied Analysis 9193--210 (2009)
  • J. Huang, X. Han, S. ZhouUniform attractors for dissipative non-autonomous Klein-Gordon-Schrodinger lattice systemsApplied Mathematics and Mechanics 301579--1607 (2009)
  • A. Ban, S. Zhou, X. HanDimension of kernel sections for damped nonautonomous wave equations with critical exponentJournal of Mathematical Physics 50012702 (2009)
  • X. Han, B. SpencerA Nonlinear model for surface segregation and solute trapping during planar film growthJournal of Applied Physics 101084302 (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)
2019FallTBDSpringOn Sabbatical leave
2018FallLinear Differential Equations (MATH2650-115)SpringLinear Differential Equations (MATH 2650)Mathematics of Interest Theory (MATH 2790)
2017FallNo TeachingSpringNo Teaching
2016FallFinancial Mathematics (MATH5870/6870)Calculus with Business Applications (MATH1680)SpringNo Teaching
2015FallApplied Mathematics (MATH 7000)Financial Mathematics (MATH 5870/6870)SpringNo Teaching
2014FallActuarial Seminar in Mathematics of Finance (MATH 4790)Mathematics Modeling: Continuous (MATH 5000/6000)SpringNo Teaching
2013FallActuarial Mathematics I (MATH5800/6800)Linear Differential Equations (MATH2650)SpringNo Teaching
2012FallFinancial Mathematics (MATH5870/6870)SpringNo Teaching
2011FallNo TeachingSpringLinear Differential Equations (MATH 2650)Mathematics of Interest Theory (MATH 2790)
2010FallNo TeachingSpringActuarial Mathematics II (MATH 5810/6810)Analysis II (MATH 5210/6210)
2009FallActuarial Mathematics I (MATH 5800/6800)Analysis I (MATH 5200/6200)SpringMathematics of Interest Theory (MATH 2790)
2008FallActuarial Seminar in Mathematics of Finance (MATH 4790)Mathematics Modeling: Continuous (MATH 5000/6000)SpringMathematics of Interest Theory (MATH 2790)
2007FallCalculus II (MATH 1620)Linear Differential Equations (MATH 2650)

Education

Ph.D.Department of Mathematics, State University of New York at Buffalo
MADepartment of Mathematics, State University of New York at Buffalo
BEThe Special Class for the Gifted Young, University of Science and Technology of China

Professional Experience

Oct 2017 - PresentProfessor of Mathematics, Auburn University, Auburn, AL
Oct 2012 - Sep 2017Associate Professor of Mathematics, Auburn University, Auburn, AL
Aug 2007 - Sep 2012Assistant Professor of Mathematics, Auburn University, Auburn, AL
May 2014 - Aug 2014Visiting Associate Professor at University of Waterloo, Canada
Jan 2013 - May 2013Visiting Scholar at IMA, Minneapolis, MN
Aug 2011 - Jun 2012Visiting 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)